InferPy: Deep Probabilistic Modeling with Tensorflow Made Easy¶

InferPy is a high-level API for probabilistic modeling written in Python and capable of running on top of Tensorflow. InferPy’s API is strongly inspired by Keras and it has a focus on enabling flexible data processing, easy-to-code probablistic modeling, scalable inference and robust model validation.

Use InferPy if you need a probabilistic programming language that:

Allows easy and fast prototyping of hierarchical probabilistic models with a simple and user friendly API inspired by Keras.
Automatically creates computational efficient batched models without the need to deal with complex tensor operations.
Run seamlessly on CPU and GPU by relying on Tensorflow, without having to learn how to use Tensorflow.

A set of examples can be found in the Probabilistic Model Zoo section.

Getting Started:¶

Installation¶

Install InferPy from PyPI:

$ python -m pip install inferpy

30 seconds to InferPy¶

The core data structures of InferPy is a probabilistic model, defined as a set of random variables with a conditional dependency structure. A random varible is an object parameterized by a set of tensors.

Let’s look at a simple non-linear probabilistic component analysis model (NLPCA). Graphically the model can be defined as follows,

Non-linear PCA¶

We start by importing the required packages and defining the constant parameters in the model.

import inferpy as inf
import tensorflow as tf

# number of components
k = 1
# size of the hidden layer in the NN
d0 = 100
# dimensionality of the data
dx = 2
# number of observations (dataset size)
N = 1000

A model can be defined by decorating any function with @inf.probmodel. The model is fully specified by the variables defined inside this function:

@inf.probmodel
def nlpca(k, d0, dx, decoder):

    with inf.datamodel():
        z = inf.Normal(tf.ones([k])*0.5, 1., name="z")    # shape = [N,k]
        output = decoder(z,d0,dx)
        x_loc = output[:,:dx]
        x_scale = tf.nn.softmax(output[:,dx:])
        x = inf.Normal(x_loc, x_scale, name="x")   # shape = [N,d]

The construct with inf.datamodel(), which resembles to the plateau notation, will replicate N times the variables enclosed, where N is the size of our data.

In the previous model, the input argument decoder must be a function implementing a neural network. This might be defined outside the model as follows.

def decoder(z,d0,dx):
    h0 = tf.layers.dense(z, d0, tf.nn.relu)
    return tf.layers.dense(h0, 2 * dx)

Now, we can instantiate our model and obtain samples (from the prior distributions).

# create an instance of the model
m = nlpca(k,d0,dx, decoder)

# Sample from priors
samples = m.sample()

In variational inference, we must defined a Q-model as follows.

@inf.probmodel
def qmodel(k):
    with inf.datamodel():
        qz_loc = inf.Parameter(tf.ones([k])*0.5, name="qz_loc")
        qz_scale = tf.math.softplus(inf.Parameter(tf.ones([k]),name="qz_scale"))

        qz = inf.Normal(qz_loc, qz_scale, name="z")

Afterwards, we define the parameters of our inference algorithm and fit the data to the model.

# set the inference algorithm
VI = inf.inference.VI(qmodel(k), epochs=5000)

# learn the parameters
m.fit({"x": x_train}, VI)

The inference method can be further configure. But, as in Keras, a core principle is to try make things reasonably simple, while allowing the user the full control if needed.

Finally, we might extract the posterior of z, which is basically the hidden representation of our data.

#extract the hidden representation
hidden_encoding = m.posterior["z"]
print(hidden_encoding.sample())

Guiding Principles¶

Features¶

The main features of InferPy are listed below.

Allows a simple definition and inference of probabilistic models containing deep neural networks.
The models that can be defined in InferPy are those that can be defined using Edward2 (i.e., tfp.edward2, whose probability distribuions are mainly inherited from the module distributions in the tensorflow-probability package.
Edward’s drawback is that for the model definition, the user has to manage complex multidimensional arrays called tensors. By contrast, in InferPy all the parameters in a model can be defined using the standard Python types (compatibility with Numpy is available as well).
InferPy directly relies on top of Edward’s inference engine and includes all the inference algorithms included in this package. As Edward’s inference engine relies on TensorFlow computing engine, InferPy also relies on it too.
Unlike Edward, our package does not require to have a strong background in the inference methods.

Architecture¶

Given the previous considerations, we might summarize the InferPy architecture as follows.

Note that InferPy can be seen as an upper layer for working with probabilistic distributions defined over tensors. Most of the interaction is done with Edward: the definitions of the random variables, the inference. However, InferPy also interacts directly with TensorFlow in some operations that are hidden to the user, e.g., the manipulation of the tensors representing the parameters of the distributions.

An additional advantage of using Edward and TensorFlow as inference engine, is that all the paralelisation details are hidden to the user. Moreover, the same code will run either in CPUs or GPUs.

Requirements¶

System¶

Currently, InferPy requires Python 3.5 or higher. For checking your default Python version, type:

$ python --version

Travis tests are performed on versions 3.5 and 3.6. Go to https://www.python.org/ for specific instructions for installing the Python interpreter in your system.

InferPy runs in any OS with the Python interpreter installed. In particular, tests have been carried out for the systems listed bellow.

Linux CentOS 7
Linux Elementary 0.4
Linux Mint 19
Linux Ubuntu 14.04 16.04 18.04
MacOS High Sierra (10.13) and Mojave (10.14)
Windows 10 Enterprise

Package Dependencies¶

For a basic usage, InferPy requires the following packages:

tensorflow>=1.12.1,<2.0
tensorflow-probability>=0.5.0,<1.0
networkx>=2.2.0<3.0
matplotlib>=2.2.3,<3.0
Keras==2.2.4
Keras-Applications==1.0.7
Keras-Preprocessing==1.0.9
protobuf==3.8.0

Guide to Probabilistic Models¶

Getting Started with Probabilistic Models¶

InferPy focuses on hierarchical probabilistic models structured in two different layers:

A prior model defining a joint distribution \(p(\mathbf{w})\) over the global parameters of the model. \(\mathbf{w}\) can be a single random variable or a bunch of random variables with any given dependency structure.
A data or observation model defining a joint conditional distribution \(p(\mathbf{x},\mathbf{z}|\mathbf{w})\) over the observed quantities \(\mathbf{x}\) and the the local hidden variables \(\mathbf{z}\) governing the observation \(\mathbf{x}\). This data model is specified in a single-sample basis. There are many models of interest without local hidden variables, in that case, we simply specify the conditional \(p(\mathbf{x}|\mathbf{w})\). Similarly, either \(\mathbf{x}\) or \(\mathbf{z}\) can be a single random variable or a bunch of random variables with any given dependency structure.

For example, a Bayesian PCA model has the following graphical structure,

Bayesian PCA¶

The prior model are the variables \(w_k\). The data model is the part of the model surrounded by the box indexed by N.

And this is how this Bayesian PCA model is denfined in InferPy:

# definition of a generic model
@inf.probmodel
def pca(k,d):
    w = inf.Normal(loc=np.zeros([k,d]), scale=1, name="w")      # shape = [k,d]
    with inf.datamodel():
        z = inf.Normal(np.ones(k),1, name="z")                # shape = [N,k]
        x = inf.Normal(z @ w , 1, name="x")                     # shape = [N,d]


# create an instance of the model
m = pca(k=1,d=2)

The with inf.datamodel() sintaxis is used to replicate the random variables contained within this construct. It follows from the so-called plateau notation to define the data generation part of a probabilistic model. Every replicated variable is conditionally idependent given the previous random variables (if any) defined outside the with statement. The plateau size will be later automatically calculated, so there is not need to specify it. Yet, this construct has an optional input parameter for specifying its size, e.g., with inf.datamodel(size=N). This should be consistent with the size of our data.

Random Variables¶

Any random variable in InferPy encapsulates an equivalent one in Edward 2, and hence it also has associated a distribution object from TensorFlow Probability. These can be accessed using the properties var and distribution respectively:

>>> x = inf.Normal(loc = 0, scale = 1)

>>> x.var
<ed.RandomVariable 'randvar_0/' shape=() dtype=float32>

>>> x.distribution
<tfp.distributions.Normal 'randvar_0/' batch_shape=() event_shape=() dtype=float32>

Even more, InferPy random variables inherit all the properties and methods from Edward2 variables or TensorFlow Probability distributions (in this order or priority). For example:

>>> x.value
<tf.Tensor 'randvar_0/sample/Reshape:0' shape=() dtype=float32>

>>> x.sample()
-0.05060442

>>> x.loc
<tf.Tensor 'randvar_0/Identity:0' shape=() dtype=float32>

In the previous code, value is inherited form the encapsulated Edward2 object while sample() and the parameter loc are obtained from the distribution object. Note that the method sample() returns an evaluated tensors. In case of desiring it not to be evaluated, simply use the input parameter tf_run as follows.

>>> x.sample(tf_run=False)
<tf.Tensor 'randvar_0/sample/Reshape:0' shape=() dtype=float32>

Following Edward’s approach, we (conceptually) partition a random variable’s shape into three groups:

Batch shape describes independent, not identically distributed draws. Namely, we may have a set of (different) parameterizations to the same distribution.
Sample shape describes independent, identically distributed draws from the distribution.
Event shape describes the shape of a single draw (event space) from the distribution; it may be dependent across dimensions.

The previous attributes can be accessed by x.batch_shape, x.sample_shape and x.event_shape, respectively. When declaring random variables, the batch_shape is obtained from the distribution parameters. For as long as possible, the parameters will be broadcasted. With this in mind, all the definitions in the following code are equivalent.

x = inf.Normal(loc = [[0.,0.],[0.,0.],[0.,0.]], scale=1)  # x.shape = [3,2]

x = inf.Normal(loc = np.zeros([3,2]), scale=1)            # x.shape = [3,2]

x = inf.Normal(loc = 0, scale=tf.ones([3,2]))             # x.shape = [3,2]

The sample_shape can be explicitly stated using the input parameter sample_shape, but this only can be done outside a model definition. Inside of inf.probmodels, the sample_shape is fixed by with inf.datamodel(size = N) (using the size argument when provided, or in runtime depending on the observed data).

x = inf.Normal(tf.ones([3,2]), 0, sample_shape=100)     # x.sample = [100,3,2]

with inf.datamodel(100):
    x = inf.Normal(tf.ones([3, 2]), 0)                  # x.sample = [100,3,2]

Finally, the event shape will only be consider in some distributions. This is the case of the multivariate Gaussian:

x = inf.MultivariateNormalDiag(loc=[1., -1], scale_diag=[1, 2.])

>>> x.event_shape
TensorShape([Dimension(2)])

>>> x.batch_shape
TensorShape([])

>>> x.sample_shape
TensorShape([])

Note that indexing over all the defined dimenensions is supported:

with inf.datamodel(size=10):
    x = inf.models.Normal(loc=tf.zeros(5), scale=1.)       # x.shape = [10,5]

y = x[7,4]                                              # y.shape = []

y2 = x[7]                                               # y2.shape = [5]

y3 = x[7,:]                                             # y2.shape = [5]

y4 = x[:,4]                                             # y4.shape = [10]

Moreover, we may use indexation for defining new variables whose indexes may be other (discrete) variables.

i = inf.Categorical(logits= tf.zeros(3))        # shape = []
mu = inf.Normal([5,1,-2], 0.)                   # shape = [3]
x = inf.Normal(mu[i], scale=1.)                 # shape = []

Probabilistic Models¶

A probabilistic model defines a joint distribution over observable and hidden variables, i.e., \(p(\mathbf{w}, \mathbf{z}, \mathbf{x})\). Note that a variable might be observable or hidden depending on the fitted data. Thus this is not specified when defining the model.

A probabilistic model is defined by decorating any function with @inf.probmodel. The model is made of any variable defined inside this function. A simple example is shown below.

@inf.probmodel
def simple(mu=0):
    # global variables
    theta = inf.Normal(mu, 0.1, name="theta")

    # local variables
    with inf.datamodel():
        x = inf.Normal(theta, 1, name="x")

Note that any variable in a model can be initialized with a name. If not provided, names generated automatically will be used. However, it is highly convenient to explicitly specify the name of a random variable because in this way it will be able to be referenced in some inference stages.

The model must be instantiated before it can be used. This is done by simple invoking the function (which will return a probmodel object).

>>> m = simple()
>>> type(m)
<class 'inferpy.models.prob_model.ProbModel'>

Now we can use the model with the prior probabilities. For example, we might get a sample or access to the distribution parameters:

>>> m.prior().sample()
{'theta': -0.074800275, 'x': array([0.07758344], dtype=float32)}

>>> m.prior().parameters()
{'theta': {'name': 'theta',
  'allow_nan_stats': True,
  'validate_args': False,
  'scale': 0.1,
  'loc': 0},
 'x': {'name': 'x',
  'allow_nan_stats': True,
  'validate_args': False,
  'scale': 1,
  'loc': 0.116854645}}

or to extract the variables:

>>> m.vars["theta"]
<inf.RandomVariable (Normal distribution) named theta/, shape=(), dtype=float32>

We can create new and different instances of our model:

>>> m2 = simple(mu=5)
>>> m==m2
False

Supported Probability Distributions¶

Supported probability distributions are located in the package inferpy.models. All of them have inferpy.models.RandomVariable as superclass. A list with all the supported distributions can be obtained as as follows.

>>> inf.models.random_variable.distributions_all
['Autoregressive', 'BatchReshape', 'Bernoulli', 'Beta', 'BetaWithSoftplusConcentration',
 'Binomial', 'Categorical', 'Cauchy', 'Chi2', 'Chi2WithAbsDf', 'ConditionalTransformedDistribution',
  'Deterministic', 'Dirichlet', 'DirichletMultinomial', 'ExpRelaxedOneHotCategorical', '
  Exponential', 'ExponentialWithSoftplusRate', 'Gamma', 'GammaGamma', 
  'GammaWithSoftplusConcentrationRate', 'Geometric', 'GaussianProcess', 
  'GaussianProcessRegressionModel', 'Gumbel', 'HalfCauchy', 'HalfNormal', 
  'HiddenMarkovModel', 'Horseshoe', 'Independent', 'InverseGamma',
   'InverseGammaWithSoftplusConcentrationRate', 'InverseGaussian', 'Kumaraswamy',
   'LinearGaussianStateSpaceModel', 'Laplace', 'LaplaceWithSoftplusScale', 'LKJ',
  'Logistic', 'LogNormal', 'Mixture', 'MixtureSameFamily', 'Multinomial',
   'MultivariateNormalDiag', 'MultivariateNormalFullCovariance', 'MultivariateNormalLinearOperator',
   'MultivariateNormalTriL', 'MultivariateNormalDiagPlusLowRank', 'MultivariateNormalDiagWithSoftplusScale',
   'MultivariateStudentTLinearOperator', 'NegativeBinomial', 'Normal', 'NormalWithSoftplusScale', 
   'OneHotCategorical', 'Pareto', 'Poisson', 'PoissonLogNormalQuadratureCompound', 'QuantizedDistribution',
   'RelaxedBernoulli', 'RelaxedOneHotCategorical', 'SinhArcsinh', 'StudentT', 'StudentTWithAbsDfSoftplusScale', 
   'StudentTProcess', 'TransformedDistribution', 'Triangular', 'TruncatedNormal', 'Uniform', 'VectorDeterministic',
   'VectorDiffeomixture', 'VectorExponentialDiag', 'VectorLaplaceDiag', 'VectorSinhArcsinhDiag', 'VonMises', 
   'VonMisesFisher', 'Wishart', 'Zipf']

Note that these are all the distributions in Edward 2 and hence in TensorFlow Probability. Their input parameters will be the same.

Guide to Approximate Inference¶

Variational Inference¶

The API defines the set of algorithms and methods used to perform inference in a probabilistic model \(p(x,z,\theta)\) (where \(x\) are the observations, \(z\) the local hidden variables, and \(\theta\) the global parameters of the model). More precisely, the inference problem reduces to compute the posterior probability over the latent variables given a data sample \(p(z,\theta | x_{train})\), because by looking at these posteriors we can uncover the hidden structure in the data. Let us consider the following model:

@inf.probmodel
def pca(k,d):
    w = inf.Normal(loc=tf.zeros([k,d]), scale=1, name="w")      # shape = [k,d]
    with inf.datamodel():
        z = inf.Normal(tf.ones([k]),1, name="z")                # shape = [N,k]
        x = inf.Normal(z @ w , 1, name="x")                     # shape = [N,d]

In this model, the posterior over the local hidden variables \(p(w_n|x_{train})\) tell us the latent vector representation of the sample \(x_n\), while the posterior over the global variables \(p(\mu|x_{train})\) tells us which is the affine transformation between the latent space and the observable space.

InferPy inherits Edward’s approach an consider approximate inference solutions,

\[q(z,\theta) \approx p(z,\theta | x_{train})\]

in which the task is to approximate the posterior \(p(z,\theta | x_{train})\) using a family of distributions, \(q(z,\theta; \lambda)\), indexed by a parameter vector \(\lambda\).

For making inference, we must define a model ‘Q’ for approximating the posterior distribution. This is also done by defining a function decorated with @inf.probmodel:

@inf.probmodel
def qmodel(k,d):
    qw_loc = inf.Parameter(tf.ones([k,d]), name="qw_loc")
    qw_scale = tf.math.softplus(inf.Parameter(tf.ones([k, d]), name="qw_scale"))
    qw = inf.Normal(qw_loc, qw_scale, name="w")

    with inf.datamodel():
        qz_loc = inf.Parameter(tf.ones([k]), name="qz_loc")
        qz_scale = tf.math.softplus(inf.Parameter(tf.ones([k]), name="qz_scale"))
        qz = inf.Normal(qz_loc, qz_scale, name="z")

In the ‘Q’ model we should include a q distribution for every non observed variable in the ‘P’ model. These varaiables are also objects of class inferpy.RandomVariable. However, their parameters might be of type inf.Parameter, which are objects encapsulating TensorFlow trainable variables.

Then, we set the parameters of the inference algorithm. In case of variational inference (VI) we must specify an instance of the ‘Q’ model and the number of epochs (i.e., iterations). For example:

# set the inference algorithm
VI = inf.inference.VI(qmodel(k=1,d=2), epochs=1000)

VI can be further configured by setting the parameter optimizer which indicates the TensorFlow optimizer to be used (AdamOptimizer by default).

Stochastic VI is similarly specified but has an additional input parameter for specifying the batch size:

SVI = inf.inference.SVI(qmodel(k=1,d=2), epochs=1000, batch_size=200)

Then we must instantiate our ‘P’ model and fit the data with the inference algorithm defined.

# create an instance of the model
m = pca(k=1,d=2)
# run the inference
m.fit({"x": x_train}, VI)

The output generated will be similar to:

epochs	 44601.14453125....................
epochs	 44196.98046875....................
epochs	 50616.359375....................
epochs	 41085.6484375....................
epochs	 30349.79296875....................

Finally we can access to the parameters of the posterior distributions:

>>> m.posterior("w").parameters()
{'name': 'w',
 'allow_nan_stats': True,
 'validate_args': False,
 'scale': array([[0.9834974 , 0.99731755]], dtype=float32),
 'loc': array([[1.7543027, 1.7246702]], dtype=float32)}

Custom Loss function¶

Following InferPy guiding principles, users can further configure the inference algorithm. For example, we might be interested in defining our own function to minimise. As an example, we define the following function taking as input parameters the random variables of the P and Q models (we assume that their sample sizes are consistent with the plates in the mdoel). Note that the output of this function must be a tensor.

def custom_elbo(pvars, qvars, **kwargs):

    # compute energy
    energy = tf.reduce_sum([tf.reduce_sum(p.log_prob(p.value)) for p in pvars.values()])

    # compute entropy
    entropy = - tf.reduce_sum([tf.reduce_sum(q.log_prob(q.value)) for q in qvars.values()])

    # compute ELBO
    ELBO = energy + entropy

    # This function will be minimized. Return minus ELBO
    return -ELBO

For using our own loss function, we simply have to pass this function to the input parameter loss in the inference method constructor. For example:

# set the inference algorithm
VI = inf.inference.VI(qmodel(k=1,d=2), loss=custom_elbo, epochs=1000)

# run the inference
m.fit({"x": x_train}, VI)

After this, the rest of the code remains unchanged.

Guide to Bayesian Deep Learning¶

InferPy inherits Edward’s approach for representing probabilistic models as (stochastic) computational graphs. As describe above, a random variable \(x\) is associated to a tensor \(x^*\) in the computational graph handled by TensorFlow, where the computations takes place. This tensor \(x^*\) contains the samples of the random variable \(x\), i.e. \(x^* \sim p(x|\theta)\). In this way, random variables can be involved in complex deterministic operations containing deep neural networks, math operations and another libraries compatible with Tensorflow (such as Keras).

Bayesian deep learning or deep probabilistic programming enbraces the idea of employing deep neural networks within a probabilistic model in order to capture complex non-linear dependencies between variables.

InferPy’s API gives support to this powerful and flexible modeling framework. Let us start by showing how a non-linear PCA can be defined by mixing tf.layers and InferPy code.

import inferpy as inf
import tensorflow as tf


# number of components
k = 1
# size of the hidden layer in the NN
d0 = 100
# dimensionality of the data
dx = 2
# number of observations (dataset size)
N = 1000


@inf.probmodel
def nlpca(k, d0, dx, decoder):

    with inf.datamodel():
        z = inf.Normal(tf.ones([k])*0.5, 1., name="z")    # shape = [N,k]
        output = decoder(z,d0,dx)
        x_loc = output[:,:dx]
        x_scale = tf.nn.softmax(output[:,dx:])
        x = inf.Normal(x_loc, x_scale, name="x")   # shape = [N,d]


def decoder(z,d0,dx):
    h0 = tf.layers.dense(z, d0, tf.nn.relu)
    return tf.layers.dense(h0, 2 * dx)


# Q-model  approximating P

@inf.probmodel
def qmodel(k):
    with inf.datamodel():
        qz_loc = inf.Parameter(tf.ones([k])*0.5, name="qz_loc")
        qz_scale = tf.math.softplus(inf.Parameter(tf.ones([k]),name="qz_scale"))

        qz = inf.Normal(qz_loc, qz_scale, name="z")


# create an instance of the model
m = nlpca(k,d0,dx, decoder)

# set the inference algorithm
VI = inf.inference.VI(qmodel(k), epochs=5000)

# learn the parameters
m.fit({"x": x_train}, VI)

#extract the hidden representation
hidden_encoding = m.posterior("z")
print(hidden_encoding.sample())

In this case, the parameters of the decoder neural network (i.e., weights) are automatically managed by TensorFlow. These parameters are them treated as model parameters and not exposed to the user. In consequence, we can not be Bayesian about them by defining specific prior distributions.

Alternatively, we could use Keras layers by simply defining an alternative decoder function as follows.

def decoder_keras(z,d0,dx):
    h0 = tf.keras.layers.Dense(d0, activation=tf.nn.relu, name="encoder_h0")
    h1 = tf.keras.layers.Dense(2*dx, name="encoder_h1")
    return h1(h0(z))


# create an instance of the model
m = nlpca(k,d0,dx, decoder_keras)

Probabilistic Model Zoo¶

In this section, we present the code for implementing some models in Inferpy.

Bayesian Linear Regression¶

Graphically, a (Bayesian) linear regression can be defined as follows,

Bayesian Linear Regression¶

The InferPy code for this model is shown below,

import inferpy as inf
import tensorflow as tf


@inf.probmodel
def linear_reg(d):
    w0 = inf.Normal(0, 1, name="w0")
    w = inf.Normal(tf.zeros([d, 1]), 1, name="w")

    with inf.datamodel():
        x = inf.Normal(tf.ones(d), 2, name="x")
        y = inf.Normal(w0 + x @ w, 1.0, name="y")


@inf.probmodel
def qmodel(d):
    qw0_loc = inf.Parameter(0., name="qw0_loc")
    qw0_scale = tf.math.softplus(inf.Parameter(1., name="qw0_scale"))
    qw0 = inf.Normal(qw0_loc, qw0_scale, name="w0")

    qw_loc = inf.Parameter(tf.zeros([d, 1]), name="qw_loc")
    qw_scale = tf.math.softplus(inf.Parameter(tf.ones([d, 1]), name="qw_scale"))
    qw = inf.Normal(qw_loc, qw_scale, name="w")


# create an instance of the model
m = linear_reg(d=2)

# create toy data
N = 1000
data = m.prior(["x", "y"], data={"w0": 0, "w": [[2], [1]]}).sample(N)

x_train = data["x"]
y_train = data["y"]

# set and run the inference
VI = inf.inference.VI(qmodel(2), epochs=10000)
m.fit({"x": x_train, "y": y_train}, VI)


# extract the parameters of the posterior
m.posterior(["w", "w0"]).parameters()

Bayesian Logistic Regression¶

Graphically, a (Bayesian) logistic regression can be defined as follows,

Bayesian Linear Regression¶

The InferPy code for this model is shown below,

# required pacakges
import inferpy as inf
import numpy as np
import tensorflow as tf


@inf.probmodel
def log_reg(d):
    w0 = inf.Normal(0., 1., name="w0")
    w = inf.Normal(np.zeros([d, 1]), np.ones([d, 1]), name="w")

    with inf.datamodel():
        x = inf.Normal(np.zeros(d), 2., name="x")  # the scale is broadcasted to shape [d] because of loc
        y = inf.Bernoulli(logits=w0 + x @ w, name="y")


@inf.probmodel
def qmodel(d):
    qw0_loc = inf.Parameter(0., name="qw0_loc")
    qw0_scale = tf.math.softplus(inf.Parameter(1., name="qw0_scale"))
    qw0 = inf.Normal(qw0_loc, qw0_scale, name="w0")

    qw_loc = inf.Parameter(tf.zeros([d, 1]), name="qw_loc")
    qw_scale = tf.math.softplus(inf.Parameter(tf.ones([d, 1]), name="qw_scale"))
    qw = inf.Normal(qw_loc, qw_scale, name="w")


# create an instance of the model
m = log_reg(d=2)

# create toy data
N = 1000
data = m.prior(["x", "y"], data={"w0": 0, "w": [[2], [1]]}).sample(N)
x_train = data["x"]
y_train = data["y"]

VI = inf.inference.VI(qmodel(2), epochs=10000)
m.fit({"x": x_train, "y": y_train}, VI)

sess = inf.get_session()
print(m.posterior("w").sample())
print(m.posterior("w").parameters())

Linear Factor Model (PCA)¶

A linear factor model allows to perform principal component analysis (PCA). Graphically, it can be defined as follows,

Linear Factor Model (PCA)¶

The InferPy code for this model is shown below,

# Generate toy data
x_train = np.concatenate([
    inf.Normal([0.0, 0.0], scale=1.).sample(int(N/2)),
    inf.Normal([10.0, 10.0], scale=1.).sample(int(N/2))
    ])
x_test = np.concatenate([
    inf.Normal([0.0, 0.0], scale=1.).sample(int(N/2)),
    inf.Normal([10.0, 10.0], scale=1.).sample(int(N/2))
    ])


# definition of a generic model
@inf.probmodel
def pca(k, d):
    beta = inf.Normal(loc=tf.zeros([k, d]),
                      scale=1, name="beta")               # shape = [k,d]

    with inf.datamodel():
        z = inf.Normal(tf.ones(k), 1, name="z")       # shape = [N,k]
        x = inf.Normal(z @ beta, 1, name="x")         # shape = [N,d]


@inf.probmodel
def qmodel(k, d):
    qbeta_loc = inf.Parameter(tf.zeros([k, d]), name="qbeta_loc")
    qbeta_scale = tf.math.softplus(inf.Parameter(tf.ones([k, d]),
                                                 name="qbeta_scale"))

    qbeta = inf.Normal(qbeta_loc, qbeta_scale, name="beta")

    with inf.datamodel():
        qz_loc = inf.Parameter(np.ones(k), name="qz_loc")
        qz_scale = tf.math.softplus(inf.Parameter(tf.ones(k),
                                                  name="qz_scale"))

        qz = inf.Normal(qz_loc, qz_scale, name="z")


# create an instance of the model and qmodel
m = pca(k=1, d=2)
q = qmodel(k=1, d=2)

# set the inference algorithm
VI = inf.inference.VI(q, epochs=2000)

# learn the parameters
m.fit({"x": x_train}, VI)

# extract the hidden encoding

Non-linear Factor Model (NLPCA)¶

Similarly to the previous model, the Non-linear PCA can be graphically defined as follows,

Non-linear PCA¶

Its code in InferPy is shown below,

import inferpy as inf
import tensorflow as tf

# definition of a generic model


# number of components
k = 1
# size of the hidden layer in the NN
d0 = 100
# dimensionality of the data
dx = 2
# number of observations (dataset size)
N = 1000


@inf.probmodel
def nlpca(k, d0, dx, decoder):

    with inf.datamodel():
        z = inf.Normal(tf.ones([k])*0.5, 1., name="z")    # shape = [N,k]
        output = decoder(z,d0,dx)
        x_loc = output[:,:dx]
        x_scale = tf.nn.softmax(output[:,dx:])
        x = inf.Normal(x_loc, x_scale, name="x")   # shape = [N,d]


def decoder(z,d0,dx):
    h0 = tf.layers.dense(z, d0, tf.nn.relu)
    return tf.layers.dense(h0, 2 * dx)


# Q-model  approximating P

@inf.probmodel
def qmodel(k):
    with inf.datamodel():
        qz_loc = inf.Parameter(tf.ones([k])*0.5, name="qz_loc")
        qz_scale = tf.math.softplus(inf.Parameter(tf.ones([k]),name="qz_scale"))

        qz = inf.Normal(qz_loc, qz_scale, name="z")


# create an instance of the model
m = nlpca(k,d0,dx, decoder)

# set the inference algorithm
VI = inf.inference.VI(qmodel(k), epochs=5000)

# learn the parameters
m.fit({"x": x_train}, VI)

# extract the hidden encoding
hidden_encoding = m.posterior("z").parameters()["loc"]

# project x_test into the reduced space (encode)
m.posterior("z", data={"x": x_test}).sample(5)

# sample from the posterior predictive (i.e., simulate values for x given the learnt hidden)
m.posterior_predictive("x").sample(5)

# decode values from the hidden representation
m.posterior_predictive("x", data={"z": [2]}).sample(5)

Variational auto-encoder (VAE)¶

Similarly to the models PCA and NLPCA, a variational autoencoder allows to perform dimensionality reduction. However a VAE will contain a neural network in the P model (decoder) and another one in the Q (encoder). Its code in InferPy is shown below,

N = 1000

# Generate toy data
x_train = np.concatenate([
    inf.Normal([0.0, 0.0], scale=1.).sample(int(N/2)),
    inf.Normal([10.0, 10.0], scale=1.).sample(int(N/2))
    ])
x_test = np.concatenate([
    inf.Normal([0.0, 0.0], scale=1.).sample(int(N/2)),
    inf.Normal([10.0, 10.0], scale=1.).sample(int(N/2))
    ])


# number of components
k = 1
# size of the hidden layer in the NN
d0 = 100
# dimensionality of the data
dx = 2
# number of observations (dataset size)
N = 1000


@inf.probmodel
def vae(k, d0, dx, decoder):

    with inf.datamodel():
        z = inf.Normal(tf.ones(k) * 0.5, 1., name="z")    # shape = [N,k]
        output = decoder(z, d0, dx)
        x_loc = output[:, :dx]
        x_scale = tf.nn.softmax(output[:, dx:])
        x = inf.Normal(x_loc, x_scale, name="x")   # shape = [N,d]


def decoder(z, d0, dx):   # k -> d0 -> 2*dx
    h0 = tf.layers.dense(z, d0, tf.nn.relu)
    return tf.layers.dense(h0, 2 * dx)


# Q-model  approximating P
def encoder(x, d0, k):  # dx -> d0 -> 2*k
    h0 = tf.layers.dense(x, d0, tf.nn.relu)
    return tf.layers.dense(h0, 2 * k)


@inf.probmodel
def qmodel(k, d0, dx, encoder):

    with inf.datamodel():
        x = inf.Normal(tf.ones(dx), 1, name="x")

        output = encoder(x, d0, k)
        qz_loc = output[:, :k]
        qz_scale = tf.nn.softmax(output[:, k:])

        qz = inf.Normal(qz_loc, qz_scale, name="z")


# create an instance of the model
m = vae(k, d0, dx, decoder)

inferpy package¶

Subpackages¶

inferpy.contextmanager package¶

Submodules¶

inferpy.contextmanager.data_model module¶

inferpy.contextmanager.data_model.datamodel(size=None)[source]¶: This context is used to declare a plateau model. Random Variables and Parameters will use a sample_shape defined by the argument size, or by the data_model.fit. If size is not specify, the default size 1, or the size specified by fit will be used.

inferpy.contextmanager.data_model.fit(size)[source]¶

inferpy.contextmanager.data_model.get_sample_shape(name)[source]¶

This function must be used inside a datamodel context (it is not checked here) If var parameters are not expanded, then expand.

inferpy.contextmanager.data_model.is_active()[source]¶

inferpy.contextmanager.evidence module¶

inferpy.contextmanager.evidence.observe(variables, data)[source]¶

inferpy.contextmanager.randvar_registry module¶

inferpy.contextmanager.randvar_registry.get_graph()[source]¶

inferpy.contextmanager.randvar_registry.get_var_parameters()[source]¶

inferpy.contextmanager.randvar_registry.get_variable(name)[source]¶

inferpy.contextmanager.randvar_registry.get_variable_or_parameter(name)[source]¶

inferpy.contextmanager.randvar_registry.init(graph=None)[source]¶

inferpy.contextmanager.randvar_registry.is_building_graph()[source]¶

inferpy.contextmanager.randvar_registry.is_default()[source]¶

inferpy.contextmanager.randvar_registry.register_parameter(p)[source]¶

inferpy.contextmanager.randvar_registry.register_variable(rv)[source]¶

inferpy.contextmanager.randvar_registry.restart_default()[source]¶

inferpy.contextmanager.randvar_registry.update_graph(rv_name=None)[source]¶

Module contents¶

inferpy.datasets package¶

Submodules¶

inferpy.datasets.mnist module¶

MNIST handwritten digits dataset.

inferpy.datasets.mnist.load_data(vectorize=True, num_instances=None, num_instances_test=None, digits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9])[source]¶

Loads the MNIST datase

Parameters

vectorize – if true, each 2D image is transformed into a 1D vector
num_instances – total number of images loaded
digits – list of integers indicating the digits to be considered

Returns

Tuple of Numpy arrays: `(x_train, y_train), (x_test, y_test)

inferpy.datasets.mnist.plot_digits(data, grid=[3, 3])[source]¶

Module contents¶

inferpy.inference package¶

Subpackages¶

inferpy.inference.variational package¶

Subpackages¶

inferpy.inference.variational.loss_functions package¶

Submodules¶

inferpy.inference.variational.loss_functions.elbo module¶

inferpy.inference.variational.loss_functions.elbo.ELBO(pvars, qvars, batch_weight=1, **kwargs)[source]¶

Compute the loss tensor from the expanded variables of p and q models. :param pvars: The dict with the expanded p random variables :type pvars: dict<inferpy.RandomVariable> :param qvars: The dict with the expanded q random variables :type qvars: dict<inferpy.RandomVariable> :param batch_weight: Weight to assign less importance to the energy, used when processing data in batches :type batch_weight: float

Returns (tf.Tensor):: The generated loss tensor

Module contents¶

inferpy.inference.variational.loss_functions.ELBO(pvars, qvars, batch_weight=1, **kwargs)[source]¶

Compute the loss tensor from the expanded variables of p and q models. :param pvars: The dict with the expanded p random variables :type pvars: dict<inferpy.RandomVariable> :param qvars: The dict with the expanded q random variables :type qvars: dict<inferpy.RandomVariable> :param batch_weight: Weight to assign less importance to the energy, used when processing data in batches :type batch_weight: float

Returns (tf.Tensor):: The generated loss tensor

Submodules¶

inferpy.inference.variational.svi module¶

class inferpy.inference.variational.svi.SVI(*args, batch_size=100, **kwargs)[source]¶

Bases: inferpy.inference.variational.vi.VI

compile(pmodel, data_size)[source]¶

create_input_data_tensor(sample_dict)[source]¶

update(sample_dict)[source]¶

inferpy.inference.variational.vi module¶

class inferpy.inference.variational.vi.VI(qmodel, loss='ELBO', optimizer='AdamOptimizer', epochs=1000)[source]¶

Bases: inferpy.inference.inference.Inference

compile(pmodel, data_size)[source]¶

log_prob(data)[source]¶

property losses¶

parameters()[source]¶

sample(size=1, data={})[source]¶

update(sample_dict)[source]¶

Module contents¶

Submodules¶

inferpy.inference.inference module¶

class inferpy.inference.inference.Inference[source]¶

Bases: object

This class implements the functionality of any Inference class.

compile(pmodel, data_size)[source]¶

log_prob(data)[source]¶

parameters()[source]¶

sample(size=1, data={})[source]¶

sum_log_prob(data)[source]¶: Computes the sum of the log probabilities of a (set of) sample(s)

update(sample_dict)[source]¶

Module contents¶

Any inference class must implement a run method, which receives a sample_dict object, and returns a dict of posterior objects (random distributions, list of samples, etc.)

class inferpy.inference.SVI(*args, batch_size=100, **kwargs)[source]¶

Bases: inferpy.inference.variational.vi.VI

compile(pmodel, data_size)[source]¶

create_input_data_tensor(sample_dict)[source]¶

update(sample_dict)[source]¶

class inferpy.inference.VI(qmodel, loss='ELBO', optimizer='AdamOptimizer', epochs=1000)[source]¶

Bases: inferpy.inference.inference.Inference

compile(pmodel, data_size)[source]¶

log_prob(data)[source]¶

property losses¶

parameters()[source]¶

sample(size=1, data={})[source]¶

update(sample_dict)[source]¶

inferpy.models package¶

Submodules¶

inferpy.models.parameter module¶

class inferpy.models.parameter.Parameter(initial_value, name=None)[source]¶

Bases: object

Random Variable parameter which can be optimized by an inference mechanism.

inferpy.models.prob_model module¶

class inferpy.models.prob_model.ProbModel(builder)[source]¶

Bases: object

Class that implements the probabilistic model functionality. It is composed of a graph, capturing the variable relationships, an OrderedDict containing the Random Variables/Parameters in order of creation, and the function which declare the Random Variables/Parameters.

expand_model(size=1)[source]¶: Create the expanded model vars using size as plate size and return the OrderedDict

fit(sample_dict, inference_method)[source]¶

plot_graph()[source]¶

posterior(target_names=None, data={})[source]¶

posterior_predictive(target_names=None, data={})[source]¶

prior(target_names=None, data={})[source]¶

update(sample_dict)[source]¶

inferpy.models.prob_model.probmodel(builder)[source]¶: Decorator to create probabilistic models. The function decorated must be a function which declares the Random Variables in the model. It is not needed that the function returns such variables (we capture them using ed.tape).

inferpy.models.random_variable module¶

inferpy.models.random_variable.Autoregressive(*args, **kwargs)¶

Create a random variable for Autoregressive.

See Autoregressive for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct an Autoregressive distribution.

Parameters

distribution_fn – Python callable which constructs a tfd.Distribution-like instance from a Tensor (e.g., sample0). The function must respect the “autoregressive property”, i.e., there exists a permutation of event such that each coordinate is a diffeomorphic function of on preceding coordinates.
sample0 – Initial input to distribution_fn; used to build the distribution in __init__ which in turn specifies this distribution’s properties, e.g., event_shape, batch_shape, dtype. If unspecified, then distribution_fn should be default constructable.
num_steps – Number of times distribution_fn is composed from samples, e.g., num_steps=2 implies distribution_fn(distribution_fn(sample0).sample(n)).sample().
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class. Default value: “Autoregressive”.

Raises

ValueError – if num_steps and num_elements(distribution_fn(sample0).event_shape) are both None.
ValueError – if num_steps < 1.

inferpy.models.random_variable.BatchReshape(*args, **kwargs)¶

Create a random variable for BatchReshape.

See BatchReshape for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct BatchReshape distribution.

Parameters

distribution – The base distribution instance to reshape. Typically an instance of Distribution.
batch_shape – Positive int-like vector-shaped Tensor representing the new shape of the batch dimensions. Up to one dimension may contain -1, meaning the remainder of the batch size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – The name to give Ops created by the initializer. Default value: “BatchReshape” + distribution.name.

Raises

ValueError – if batch_shape is not a vector.
ValueError – if batch_shape has non-positive elements.
ValueError – if batch_shape size is not the same as a distribution.batch_shape size.

inferpy.models.random_variable.Bernoulli(*args, **kwargs)¶

Create a random variable for Bernoulli.

See Bernoulli for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Bernoulli distributions.

Parameters

logits – An N-D Tensor representing the log-odds of a 1 event. Each entry in the Tensor parametrizes an independent Bernoulli distribution where the probability of an event is sigmoid(logits). Only one of logits or probs should be passed in.
probs – An N-D Tensor representing the probability of a 1 event. Each entry in the Tensor parameterizes an independent Bernoulli distribution. Only one of logits or probs should be passed in.
dtype – The type of the event samples. Default: int32.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If p and logits are passed, or if neither are passed.

inferpy.models.random_variable.Beta(*args, **kwargs)¶

Create a random variable for Beta.

See Beta for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Beta distributions.

Parameters

concentration1 – Positive floating-point Tensor indicating mean number of successes; aka “alpha”. Implies self.dtype and self.batch_shape, i.e., concentration1.shape = [N1, N2, …, Nm] = self.batch_shape.
concentration0 – Positive floating-point Tensor indicating mean number of failures; aka “beta”. Otherwise has same semantics as concentration1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Binomial(*args, **kwargs)¶

Create a random variable for Binomial.

See Binomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Binomial distributions.

Parameters

total_count – Non-negative floating point tensor with shape broadcastable to [N1,…, Nm] with m >= 0 and the same dtype as probs or logits. Defines this as a batch of N1 x … x Nm different Binomial distributions. Its components should be equal to integer values.
logits – Floating point tensor representing the log-odds of a positive event with shape broadcastable to [N1,…, Nm] m >= 0, and the same dtype as total_count. Each entry represents logits for the probability of success for independent Binomial distributions. Only one of logits or probs should be passed in.
probs – Positive floating point tensor with shape broadcastable to [N1,…, Nm] m >= 0, probs in [0, 1]. Each entry represents the probability of success for independent Binomial distributions. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Blockwise(*args, **kwargs)¶

Create a random variable for Blockwise.

See Blockwise for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the Blockwise distribution.

Parameters

distributions – Python list of tfp.distributions.Distribution instances. All distribution instances must have the same batch_shape and all must have event_ndims==1, i.e., be vector-variate distributions.
dtype_override – samples of distributions will be cast to this dtype. If unspecified, all distributions must have the same dtype. Default value: None (i.e., do not cast).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Categorical(*args, **kwargs)¶

Create a random variable for Categorical.

See Categorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize Categorical distributions using class log-probabilities.

Parameters

logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
dtype – The type of the event samples (default: int32).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Cauchy(*args, **kwargs)¶

Create a random variable for Cauchy.

See Cauchy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Cauchy distributions.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor; the modes of the distribution(s).
scale – Floating point tensor; the locations of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.random_variable.Chi(*args, **kwargs)¶

Create a random variable for Chi.

See Chi for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Chi distributions with parameter df.

Parameters

df – Floating point tensor, the degrees of freedom of the distribution(s). df must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class. Default value: ‘Chi’.

inferpy.models.random_variable.Chi2(*args, **kwargs)¶

Create a random variable for Chi2.

See Chi2 for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Chi2 distributions with parameter df.

Parameters

df – Floating point tensor, the degrees of freedom of the distribution(s). df must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Chi2WithAbsDf(*args, **kwargs)¶

Create a random variable for Chi2WithAbsDf.

See Chi2WithAbsDf for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

DEPRECATED FUNCTION

Warning: THIS FUNCTION IS DEPRECATED. It will be removed after 2019-06-05. Instructions for updating: Chi2WithAbsDf is deprecated, use Chi2(df=tf.floor(tf.abs(df))) instead.

inferpy.models.random_variable.ConditionalDistribution(*args, **kwargs)¶

Create a random variable for ConditionalDistribution.

See ConditionalDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.random_variable.ConditionalTransformedDistribution(*args, **kwargs)¶

Create a random variable for ConditionalTransformedDistribution.

See ConditionalTransformedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Transformed Distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
bijector – The object responsible for calculating the transformation. Typically an instance of Bijector.
batch_shape – integer vector Tensor which overrides distribution batch_shape; valid only if distribution.is_scalar_batch().
event_shape – integer vector Tensor which overrides distribution event_shape; valid only if distribution.is_scalar_event().
kwargs_split_fn –
Python callable which takes a kwargs dict and returns a tuple of kwargs dict`s for each of the `distribution and bijector parameters respectively. Default value: _default_kwargs_split_fn (i.e.,

`lambda kwargs: (kwargs.get(‘distribution_kwargs’, {}),
kwargs.get(‘bijector_kwargs’, {}))`)
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
parameters – Locals dict captured by subclass constructor, to be used for copy/slice re-instantiation operations.
name – Python str name prefixed to Ops created by this class. Default: bijector.name + distribution.name.

inferpy.models.random_variable.Deterministic(*args, **kwargs)¶

Create a random variable for Deterministic.

See Deterministic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a scalar Deterministic distribution.

The atol and rtol parameters allow for some slack in pmf, cdf computations, e.g. due to floating-point error.

``` pmf(x; loc)

```

Parameters

loc – Numeric Tensor of shape [B1, …, Bb], with b >= 0. The point (or batch of points) on which this distribution is supported.
atol – Non-negative Tensor of same dtype as loc and broadcastable shape. The absolute tolerance for comparing closeness to loc. Default is 0.
rtol – Non-negative Tensor of same dtype as loc and broadcastable shape. The relative tolerance for comparing closeness to loc. Default is 0.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Dirichlet(*args, **kwargs)¶

Create a random variable for Dirichlet.

See Dirichlet for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Dirichlet distributions.

Parameters

concentration – Positive floating-point Tensor indicating mean number of class occurrences; aka “alpha”. Implies self.dtype, and self.batch_shape, self.event_shape, i.e., if concentration.shape = [N1, N2, …, Nm, k] then batch_shape = [N1, N2, …, Nm] and event_shape = [k].
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.DirichletMultinomial(*args, **kwargs)¶

Create a random variable for DirichletMultinomial.

See DirichletMultinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of DirichletMultinomial distributions.

Parameters

total_count – Non-negative floating point tensor, whose dtype is the same as concentration. The shape is broadcastable to [N1,…, Nm] with m >= 0. Defines this as a batch of N1 x … x Nm different Dirichlet multinomial distributions. Its components should be equal to integer values.
concentration – Positive floating point tensor, whose dtype is the same as n with shape broadcastable to [N1,…, Nm, K] m >= 0. Defines this as a batch of N1 x … x Nm different K class Dirichlet multinomial distributions.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Distribution(*args, **kwargs)¶

Create a random variable for Distribution.

See Distribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.random_variable.Empirical(*args, **kwargs)¶

Create a random variable for Empirical.

See Empirical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize Empirical distributions.

Parameters

samples – Numeric Tensor of shape [B1, …, Bk, S, E1, …, En]`, k, n >= 0. Samples or batches of samples on which the distribution is based. The first k dimensions index into a batch of independent distributions. Length of S dimension determines number of samples in each multiset. The last n dimension represents samples for each distribution. n is specified by argument event_ndims.
event_ndims – Python int32, default 0. number of dimensions for each event. When 0 this distribution has scalar samples. When 1 this distribution has vector-like samples.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if the rank of samples < event_ndims + 1.

inferpy.models.random_variable.ExpRelaxedOneHotCategorical(*args, **kwargs)¶

Create a random variable for ExpRelaxedOneHotCategorical.

See ExpRelaxedOneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize ExpRelaxedOneHotCategorical using class log-probabilities.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of ExpRelaxedCategorical distributions. The temperature should be positive.
logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of ExpRelaxedCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of ExpRelaxedCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Exponential(*args, **kwargs)¶

Create a random variable for Exponential.

See Exponential for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Exponential distribution with parameter rate.

Parameters

rate – Floating point tensor, equivalent to 1 / mean. Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.FiniteDiscrete(*args, **kwargs)¶

Create a random variable for FiniteDiscrete.

See FiniteDiscrete for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a finite discrete contribution.

Parameters

outcomes – A 1-D floating or integer Tensor, representing a list of possible outcomes in strictly ascending order.
logits – A floating N-D Tensor, N >= 1, representing the log probabilities of a set of FiniteDiscrete distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each discrete value. Only one of logits or probs should be passed in.
probs – A floating N-D Tensor, N >= 1, representing the probabilities of a set of FiniteDiscrete distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each discrete value. Only one of logits or probs should be passed in.
rtol – Tensor with same dtype as outcomes. The relative tolerance for floating number comparison. Only effective when outcomes is a floating Tensor. Default is 10 * eps.
atol – Tensor with same dtype as outcomes. The absolute tolerance for floating number comparison. Only effective when outcomes is a floating Tensor. Default is 10 * eps.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value ‘NaN’ to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Gamma(*args, **kwargs)¶

Create a random variable for Gamma.

See Gamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Gamma with concentration and rate parameters.

The parameters concentration and rate must be shaped in a way that supports broadcasting (e.g. concentration + rate is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
rate – Floating point tensor, the inverse scale params of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and rate are different dtypes.

inferpy.models.random_variable.GammaGamma(*args, **kwargs)¶

Create a random variable for GammaGamma.

See GammaGamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initializes a batch of Gamma-Gamma distributions.

The parameters concentration and rate must be shaped in a way that supports broadcasting (e.g. concentration + mixing_concentration + mixing_rate is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
mixing_concentration – Floating point tensor, the concentration params of the mixing Gamma distribution(s). Must contain only positive values.
mixing_rate – Floating point tensor, the rate params of the mixing Gamma distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and rate are different dtypes.

inferpy.models.random_variable.GaussianProcess(*args, **kwargs)¶

Create a random variable for GaussianProcess.

See GaussianProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a GaussianProcess Distribution.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the GP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to a e-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
mean_fn – Python callable that acts on index_points to produce a (batch of) vector(s) of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies constant zero function.
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “GaussianProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.random_variable.GaussianProcessRegressionModel(*args, **kwargs)¶

Create a random variable for GaussianProcessRegressionModel.

See GaussianProcessRegressionModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a GaussianProcessRegressionModel instance.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite collection, or batch of collections, of points in the index set over which the GP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to an e-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
observation_index_points – float Tensor representing finite collection, or batch of collections, of points in the index set for which some data has been observed. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims, and e is the number (size) of index points in each batch. [b1, …, bB, e] must be broadcastable with the shape of observations, and [b1, …, bB] must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc). The default value is None, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance predictive_noise_variance).
observations – float Tensor representing collection, or batch of collections, of observations corresponding to observation_index_points. Shape has the form [b1, …, bB, e], which must be brodcastable with the batch and example shapes of observation_index_points. The batch shape [b1, …, bB] must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). The default value is None, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance predictive_noise_variance).
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
predictive_noise_variance – float Tensor representing the variance in the posterior predictive model. If None, we simply re-use observation_noise_variance for the posterior predictive noise. If set explicitly, however, we use this value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
mean_fn – Python callable that acts on index_points to produce a collection, or batch of collections, of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies the constant zero function.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: ‘GaussianProcessRegressionModel’.

Raises

ValueError – if either - only one of observations and observation_index_points is given, or - mean_fn is not None and not callable.

inferpy.models.random_variable.Geometric(*args, **kwargs)¶

Create a random variable for Geometric.

See Geometric for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Geometric distributions.

Parameters

logits – Floating-point Tensor with shape [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents logits for the probability of success for independent Geometric distributions and must be in the range (-inf, inf]. Only one of logits or probs should be specified.
probs – Positive floating-point Tensor with shape [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents the probability of success for independent Geometric distributions and must be in the range (0, 1]. Only one of logits or probs should be specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Gumbel(*args, **kwargs)¶

Create a random variable for Gumbel.

See Gumbel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Gumbel distributions with location and scale loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor, the means of the distribution(s).
scale – Floating point tensor, the scales of the distribution(s). scale must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Gumbel’.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.random_variable.HalfCauchy(*args, **kwargs)¶

Create a random variable for HalfCauchy.

See HalfCauchy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a half-Cauchy distribution with loc and scale.

Parameters

loc – Floating-point Tensor; the location(s) of the distribution(s).
scale – Floating-point Tensor; the scale(s) of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘HalfCauchy’.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.random_variable.HalfNormal(*args, **kwargs)¶

Create a random variable for HalfNormal.

See HalfNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct HalfNormals with scale scale.

Parameters

scale – Floating point tensor; the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.HiddenMarkovModel(*args, **kwargs)¶

Create a random variable for HiddenMarkovModel.

See HiddenMarkovModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize hidden Markov model.

Parameters

initial_distribution – A Categorical-like instance. Determines probability of first hidden state in Markov chain. The number of categories must match the number of categories of transition_distribution as well as both the rightmost batch dimension of transition_distribution and the rightmost batch dimension of observation_distribution.
transition_distribution – A Categorical-like instance. The rightmost batch dimension indexes the probability distribution of each hidden state conditioned on the previous hidden state.
observation_distribution – A tfp.distributions.Distribution-like instance. The rightmost batch dimension indexes the distribution of each observation conditioned on the corresponding hidden state.
num_steps – The number of steps taken in Markov chain. A python int.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: “HiddenMarkovModel”.

Raises

ValueError – if num_steps is not at least 1.
ValueError – if initial_distribution does not have scalar event_shape.
ValueError – if transition_distribution does not have scalar event_shape.
ValueError – if transition_distribution and observation_distribution are fully defined but don’t have matching rightmost dimension.

inferpy.models.random_variable.Horseshoe(*args, **kwargs)¶

Create a random variable for Horseshoe.

See Horseshoe for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Horseshoe distribution with scale.

Parameters

scale – Floating point tensor; the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e., do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Horseshoe’.

inferpy.models.random_variable.Independent(*args, **kwargs)¶

Create a random variable for Independent.

See Independent for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Independent distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
reinterpreted_batch_ndims – Scalar, integer number of rightmost batch dims which will be regarded as event dims. When None all but the first batch axis (batch axis 0) will be transferred to event dimensions (analogous to tf.layers.flatten).
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
name – The name for ops managed by the distribution. Default value: Independent + distribution.name.

Raises

ValueError – if reinterpreted_batch_ndims exceeds distribution.batch_ndims

inferpy.models.random_variable.InverseGamma(*args, **kwargs)¶

Create a random variable for InverseGamma.

See InverseGamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct InverseGamma with concentration and scale parameters. (deprecated arguments)

Warning: SOME ARGUMENTS ARE DEPRECATED: (rate). They will be removed after 2019-05-08. Instructions for updating: The rate parameter is deprecated. Use scale instead.The rate parameter was always interpreted as a scale parameter, but erroneously misnamed.

The parameters concentration and scale must be shaped in a way that supports broadcasting (e.g. concentration + scale is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
scale – Floating point tensor, the scale params of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
rate – Deprecated (mis-named) alias for scale.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and scale are different dtypes.

inferpy.models.random_variable.InverseGaussian(*args, **kwargs)¶

Create a random variable for InverseGaussian.

See InverseGaussian for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs inverse Gaussian distribution with loc and concentration.

Parameters

loc – Floating-point Tensor, the loc params. Must contain only positive values.
concentration – Floating-point Tensor, the concentration params. Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘InverseGaussian’.

inferpy.models.random_variable.JointDistribution(*args, **kwargs)¶

Create a random variable for JointDistribution.

See JointDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.random_variable.JointDistributionCoroutine(*args, **kwargs)¶

Create a random variable for JointDistributionCoroutine.

See JointDistributionCoroutine for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionCoroutine distribution.

Parameters

model – A generator that yields a sequence of tfd.Distribution-like instances.
sample_dtype – Samples from this distribution will be structured like tf.nest.pack_sequence_as(sample_dtype, list_). sample_dtype is only used for tf.nest.pack_sequence_as structuring of outputs, never casting (which is the responsibility of the component distributions). Default value: None (i.e., tuple).
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionCoroutine”).

inferpy.models.random_variable.JointDistributionNamed(*args, **kwargs)¶

Create a random variable for JointDistributionNamed.

See JointDistributionNamed for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionNamed distribution.

Parameters

model – Python dict or namedtuple of distribution-making functions each with required args corresponding only to other keys.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionNamed”).

inferpy.models.random_variable.JointDistributionSequential(*args, **kwargs)¶

Create a random variable for JointDistributionSequential.

See JointDistributionSequential for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionSequential distribution.

Parameters

model – Python list of either tfd.Distribution instances and/or lambda functions which take the k previous distributions and returns a new tfd.Distribution instance.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionSequential”).

class inferpy.models.random_variable.Kind[source]¶

Bases: enum.IntEnum

An enumeration.

GLOBAL_HIDDEN = 0¶

GLOBAL_OBSERVED = 1¶

LOCAL_HIDDEN = 2¶

LOCAL_OBSERVED = 3¶

inferpy.models.random_variable.Kumaraswamy(*args, **kwargs)¶

Create a random variable for Kumaraswamy.

See Kumaraswamy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Kumaraswamy distributions.

Parameters

concentration1 – Positive floating-point Tensor indicating mean number of successes; aka “alpha”. Implies self.dtype and self.batch_shape, i.e., concentration1.shape = [N1, N2, …, Nm] = self.batch_shape.
concentration0 – Positive floating-point Tensor indicating mean number of failures; aka “beta”. Otherwise has same semantics as concentration1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.LKJ(*args, **kwargs)¶

Create a random variable for LKJ.

See LKJ for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct LKJ distributions.

Parameters

dimension – Python int. The dimension of the correlation matrices to sample.
concentration – float or double Tensor. The positive concentration parameter of the LKJ distributions. The pdf of a sample matrix X is proportional to det(X) ** (concentration - 1).
input_output_cholesky – Python bool. If True, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is True, input to log_prob is presumed of Cholesky form and output from sample is of Cholesky form. Setting this argument to True is purely a computational optimization and does not change the underlying distribution. Additionally, validation checks which are only defined on the multiplied-out form are omitted, even if validate_args is True. Default value: False (i.e., input/output does not have Cholesky semantics).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If dimension is negative.

inferpy.models.random_variable.Laplace(*args, **kwargs)¶

Create a random variable for Laplace.

See Laplace for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Laplace distribution with parameters loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g., loc / scale is a valid operation).

Parameters

loc – Floating point tensor which characterizes the location (center) of the distribution.
scale – Positive floating point tensor which characterizes the spread of the distribution.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale are of different dtype.

inferpy.models.random_variable.LinearGaussianStateSpaceModel(*args, **kwargs)¶

Create a random variable for LinearGaussianStateSpaceModel.

See LinearGaussianStateSpaceModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a `LinearGaussianStateSpaceModel.

Parameters

num_timesteps – Integer Tensor total number of timesteps.
transition_matrix – A transition operator, represented by a Tensor or LinearOperator of shape [latent_size, latent_size], or by a callable taking as argument a scalar integer Tensor t and returning a Tensor or LinearOperator representing the transition operator from latent state at time t to time t + 1.
transition_noise – An instance of tfd.MultivariateNormalLinearOperator with event shape [latent_size], representing the mean and covariance of the transition noise model, or a callable taking as argument a scalar integer Tensor t and returning such a distribution representing the noise in the transition from time t to time t + 1.
observation_matrix – An observation operator, represented by a Tensor or LinearOperator of shape [observation_size, latent_size], or by a callable taking as argument a scalar integer Tensor t and returning a timestep-specific Tensor or LinearOperator.
observation_noise – An instance of tfd.MultivariateNormalLinearOperator with event shape [observation_size], representing the mean and covariance of the observation noise model, or a callable taking as argument a scalar integer Tensor t and returning a timestep-specific noise model.
initial_state_prior – An instance of MultivariateNormalLinearOperator representing the prior distribution on latent states; must have event shape [latent_size].
initial_step – optional int specifying the time of the first modeled timestep. This is added as an offset when passing timesteps t to (optional) callables specifying timestep-specific transition and observation models.
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

inferpy.models.random_variable.LogNormal(*args, **kwargs)¶

Create a random variable for LogNormal.

See LogNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a log-normal distribution.

The LogNormal distribution models positive-valued random variables whose logarithm is normally distributed with mean loc and standard deviation scale. It is constructed as the exponential transformation of a Normal distribution.

Parameters

loc – Floating-point Tensor; the means of the underlying Normal distribution(s).
scale – Floating-point Tensor; the stddevs of the underlying Normal distribution(s).
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

inferpy.models.random_variable.Logistic(*args, **kwargs)¶

Create a random variable for Logistic.

See Logistic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Logistic distributions with mean and scale loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor, the means of the distribution(s).
scale – Floating point tensor, the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – The name to give Ops created by the initializer.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.random_variable.Mixture(*args, **kwargs)¶

Create a random variable for Mixture.

See Mixture for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a Mixture distribution.

A Mixture is defined by a Categorical (cat, representing the mixture probabilities) and a list of Distribution objects all having matching dtype, batch shape, event shape, and continuity properties (the components).

The num_classes of cat must be possible to infer at graph construction time and match len(components).

Parameters

cat – A Categorical distribution instance, representing the probabilities of distributions.
components – A list or tuple of Distribution instances. Each instance must have the same type, be defined on the same domain, and have matching event_shape and batch_shape.
validate_args – Python bool, default False. If True, raise a runtime error if batch or event ranks are inconsistent between cat and any of the distributions. This is only checked if the ranks cannot be determined statically at graph construction time.
allow_nan_stats –
Boolean, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any

batch member. If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
use_static_graph – Calls to sample will not rely on dynamic tensor indexing, allowing for some static graph compilation optimizations, but at the expense of sampling all underlying distributions in the mixture. (Possibly useful when running on TPUs). Default value: False (i.e., use dynamic indexing).
name – A name for this distribution (optional).

Raises

TypeError – If cat is not a Categorical, or components is not a list or tuple, or the elements of components are not instances of Distribution, or do not have matching dtype.
ValueError – If components is an empty list or tuple, or its elements do not have a statically known event rank. If cat.num_classes cannot be inferred at graph creation time, or the constant value of cat.num_classes is not equal to len(components), or all components and cat do not have matching static batch shapes, or all components do not have matching static event shapes.

inferpy.models.random_variable.MixtureSameFamily(*args, **kwargs)¶

Create a random variable for MixtureSameFamily.

See MixtureSameFamily for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a MixtureSameFamily distribution.

Parameters

mixture_distribution – tfp.distributions.Categorical-like instance. Manages the probability of selecting components. The number of categories must match the rightmost batch dimension of the components_distribution. Must have either scalar batch_shape or batch_shape matching components_distribution.batch_shape[:-1].
components_distribution – tfp.distributions.Distribution-like instance. Right-most batch dimension indexes components.
reparameterize –
Python bool, default False. Whether to reparameterize samples of the distribution using implicit reparameterization gradients [(Figurnov et al., 2018)][1]. The gradients for the mixture logits are equivalent to the ones described by [(Graves, 2016)][2]. The gradients for the components parameters are also computed using implicit reparameterization (as opposed to ancestral sampling), meaning that all components are updated every step. Only works when:
1. components_distribution is fully reparameterized;
(2) components_distribution is either a scalar distribution or fully factorized (tfd.Independent applied to a scalar distribution); (3) batch shape has a known rank.
Experimental, may be slow and produce infs/NaNs.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if not dtype_util.is_integer(mixture_distribution.dtype).
ValueError – if mixture_distribution does not have scalar event_shape.
ValueError – if mixture_distribution.batch_shape and components_distribution.batch_shape[:-1] are both fully defined and the former is neither scalar nor equal to the latter.
ValueError – if mixture_distribution categories does not equal components_distribution rightmost batch shape.

#### References

[1]: Michael Figurnov, Shakir Mohamed and Andriy Mnih. Implicit: reparameterization gradients. In _Neural Information Processing Systems_, 2018. https://arxiv.org/abs/1805.08498
[2]: Alex Graves. Stochastic Backpropagation through Mixture Density: Distributions. _arXiv_, 2016. https://arxiv.org/abs/1607.05690

inferpy.models.random_variable.Multinomial(*args, **kwargs)¶

Create a random variable for Multinomial.

See Multinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Multinomial distributions.

Parameters

total_count – Non-negative floating point tensor with shape broadcastable to [N1,…, Nm] with m >= 0. Defines this as a batch of N1 x … x Nm different Multinomial distributions. Its components should be equal to integer values.
logits – Floating point tensor representing unnormalized log-probabilities of a positive event with shape broadcastable to [N1,…, Nm, K] m >= 0, and the same dtype as total_count. Defines this as a batch of N1 x … x Nm different K class Multinomial distributions. Only one of logits or probs should be passed in.
probs – Positive floating point tensor with shape broadcastable to [N1,…, Nm, K] m >= 0 and same dtype as total_count. Defines this as a batch of N1 x … x Nm different K class Multinomial distributions. probs’s components in the last portion of its shape should sum to 1. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.MultivariateNormalDiag(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiag.

See MultivariateNormalDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.random_variable.MultivariateNormalDiagPlusLowRank(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiagPlusLowRank.

See MultivariateNormalDiagPlusLowRank for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

```none scale = diag(scale_diag + scale_identity_multiplier ones(k)) +

```

where:

scale_diag.shape = [k],
scale_identity_multiplier.shape = [],
scale_perturb_factor.shape = [k, r], typically k >> r, and,
scale_perturb_diag.shape = [r].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_perturb_factor – Floating-point Tensor representing a rank-r perturbation added to scale. May have shape [B1, …, Bb, k, r], b >= 0, and characterizes b-batches of rank-r updates to scale. When None, no rank-r update is added to scale.
scale_perturb_diag – Floating-point Tensor representing a diagonal matrix inside the rank-r perturbation added to scale. May have shape [B1, …, Bb, r], b >= 0, and characterizes b-batches of r x r diagonal matrices inside the perturbation added to scale. When None, an identity matrix is used inside the perturbation. Can only be specified if scale_perturb_factor is also specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.random_variable.MultivariateNormalDiagWithSoftplusScale(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiagWithSoftplusScale.

See MultivariateNormalDiagWithSoftplusScale for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

DEPRECATED FUNCTION

Warning: THIS FUNCTION IS DEPRECATED. It will be removed after 2019-06-05. Instructions for updating: MultivariateNormalDiagWithSoftplusScale is deprecated, use MultivariateNormalDiag(loc=loc, scale_diag=tf.nn.softplus(scale_diag)) instead.

inferpy.models.random_variable.MultivariateNormalFullCovariance(*args, **kwargs)¶

Create a random variable for MultivariateNormalFullCovariance.

See MultivariateNormalFullCovariance for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and covariance_matrix arguments.

The event_shape is given by last dimension of the matrix implied by covariance_matrix. The last dimension of loc (if provided) must broadcast with this.

A non-batch covariance_matrix matrix is a k x k symmetric positive definite matrix. In other words it is (real) symmetric with all eigenvalues strictly positive.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
covariance_matrix – Floating-point, symmetric positive definite Tensor of same dtype as loc. The strict upper triangle of covariance_matrix is ignored, so if covariance_matrix is not symmetric no error will be raised (unless validate_args is True). covariance_matrix has shape [B1, …, Bb, k, k] where b >= 0 and k is the event size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if neither loc nor covariance_matrix are specified.

inferpy.models.random_variable.MultivariateNormalLinearOperator(*args, **kwargs)¶

Create a random variable for MultivariateNormalLinearOperator.

See MultivariateNormalLinearOperator for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale – Instance of LinearOperator with same dtype as loc and shape [B1, …, Bb, k, k].
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

Raises

ValueError – if scale is unspecified.
TypeError – if not scale.dtype.is_floating

inferpy.models.random_variable.MultivariateNormalTriL(*args, **kwargs)¶

Create a random variable for MultivariateNormalTriL.

See MultivariateNormalTriL for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

`none scale = scale_tril `

where scale_tril is lower-triangular k x k matrix with non-zero diagonal, i.e., tf.diag_part(scale_tril) != 0.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_tril – Floating-point, lower-triangular Tensor with non-zero diagonal elements. scale_tril has shape [B1, …, Bb, k, k] where b >= 0 and k is the event size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if neither loc nor scale_tril are specified.

inferpy.models.random_variable.MultivariateStudentTLinearOperator(*args, **kwargs)¶

Create a random variable for MultivariateStudentTLinearOperator.

See MultivariateStudentTLinearOperator for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Student’s t-distribution on R^k.

The batch_shape is the broadcast shape between df, loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc must broadcast with this.

Additional leading dimensions (if any) will index batches.

Parameters

df – A positive floating-point Tensor. Has shape [B1, …, Bb] where b >= 0.
loc – Floating-point Tensor. Has shape [B1, …, Bb, k] where k is the event size.
scale – Instance of LinearOperator with a floating dtype and shape [B1, …, Bb, k, k].
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/variance/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

Raises

TypeError – if not scale.dtype.is_floating.
ValueError – if not scale.is_positive_definite.

inferpy.models.random_variable.NegativeBinomial(*args, **kwargs)¶

Create a random variable for NegativeBinomial.

See NegativeBinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct NegativeBinomial distributions.

Parameters

total_count – Non-negative floating-point Tensor with shape broadcastable to [B1,…, Bb] with b >= 0 and the same dtype as probs or logits. Defines this as a batch of N1 x … x Nm different Negative Binomial distributions. In practice, this represents the number of negative Bernoulli trials to stop at (the total_count of failures), but this is still a valid distribution when total_count is a non-integer.
logits – Floating-point Tensor with shape broadcastable to [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents logits for the probability of success for independent Negative Binomial distributions and must be in the open interval (-inf, inf). Only one of logits or probs should be specified.
probs – Positive floating-point Tensor with shape broadcastable to [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents the probability of success for independent Negative Binomial distributions and must be in the open interval (0, 1). Only one of logits or probs should be specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Normal(*args, **kwargs)¶

Create a random variable for Normal.

See Normal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Normal distributions with mean and stddev loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor; the means of the distribution(s).
scale – Floating point tensor; the stddevs of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.random_variable.OneHotCategorical(*args, **kwargs)¶

Create a random variable for OneHotCategorical.

See OneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize OneHotCategorical distributions using class log-probabilities.

Parameters

logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
dtype – The type of the event samples (default: int32).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Pareto(*args, **kwargs)¶

Create a random variable for Pareto.

See Pareto for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Pareto distribution with concentration and scale.

Parameters

concentration – Floating point tensor. Must contain only positive values.
scale – Floating point tensor, equivalent to mode. scale also restricts the domain of this distribution to be in [scale, inf). Must contain only positive values. Default value: 1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Pareto’.

inferpy.models.random_variable.Poisson(*args, **kwargs)¶

Create a random variable for Poisson.

See Poisson for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Poisson distributions.

Parameters

rate – Floating point tensor, the rate parameter. rate must be positive. Must specify exactly one of rate and log_rate.
log_rate – Floating point tensor, the log of the rate parameter. Must specify exactly one of rate and log_rate.
interpolate_nondiscrete – Python bool. When False, log_prob returns -inf (and prob returns 0) for non-integer inputs. When True, log_prob evaluates the continuous function k * log_rate - lgamma(k+1) - rate, which matches the Poisson pmf at integer arguments k (note that this function is not itself a normalized probability log-density). Default value: True.
validate_args – Python bool. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if none or both of rate, log_rate are specified.
TypeError – if rate is not a float-type.
TypeError – if log_rate is not a float-type.

inferpy.models.random_variable.PoissonLogNormalQuadratureCompound(*args, **kwargs)¶

Create a random variable for PoissonLogNormalQuadratureCompound.

See PoissonLogNormalQuadratureCompound for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the PoissonLogNormalQuadratureCompound`.

Note: probs returned by (optional) quadrature_fn are presumed to be either a length-quadrature_size vector or a batch of vectors in 1-to-1 correspondence with the returned grid. (I.e., broadcasting is only partially supported.)

Parameters

loc – float-like (batch of) scalar Tensor; the location parameter of the LogNormal prior.
scale – float-like (batch of) scalar Tensor; the scale parameter of the LogNormal prior.
quadrature_size – Python int scalar representing the number of quadrature points.
quadrature_fn – Python callable taking loc, scale, quadrature_size, validate_args and returning tuple(grid, probs) representing the LogNormal grid and corresponding normalized weight. normalized) weight. Default value: quadrature_scheme_lognormal_quantiles.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if quadrature_grid and quadrature_probs have different base dtype.

inferpy.models.random_variable.QuantizedDistribution(*args, **kwargs)¶

Create a random variable for QuantizedDistribution.

See QuantizedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Quantized Distribution representing Y = ceiling(X).

Some properties are inherited from the distribution defining X. Example: allow_nan_stats is determined for this QuantizedDistribution by reading the distribution.

Parameters

distribution – The base distribution class to transform. Typically an instance of Distribution.
low – Tensor with same dtype as this distribution and shape able to be added to samples. Should be a whole number. Default None. If provided, base distribution’s prob should be defined at low.
high – Tensor with same dtype as this distribution and shape able to be added to samples. Should be a whole number. Default None. If provided, base distribution’s prob should be defined at high - 1. high must be strictly greater than low.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – If dist_cls is not a subclass of Distribution or continuous.
NotImplementedError – If the base distribution does not implement cdf.

class inferpy.models.random_variable.RandomVariable(var, name, is_datamodel, ed_cls, var_args, var_kwargs, sample_shape, is_observed, observed_value)[source]¶

Bases: object

Class for random variables. It encapsulates the Random Variable from edward2, and additional properties.

It creates a variable generator. It must be a function without parameters, that creates a new Random Variable from edward2. It is used to define edward2 models as functions. Also, it is useful to define models using the intercept function.
The first time the var property is used, it creates a var using the variable generator.

build_in_session(sess)[source]¶: Allow to build a copy of the random variable but running previously each parameter in the tf session. This way, it uses the value of each tf variable or placeholder as a tensor, not as a tf variable or placeholder. If this random variable is a ed random variable directly assigned to .var, we cannot re-create it. In this case, return self. :param sess: tf session used to run each parameter used to build this random variable. :returns: the random variable object

copy()[source]¶: Makes a of the current random variable where the distribution parameters are fixed. :return: new object of class RandomVariable

property type¶

inferpy.models.random_variable.RelaxedBernoulli(*args, **kwargs)¶

Create a random variable for RelaxedBernoulli.

See RelaxedBernoulli for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct RelaxedBernoulli distributions.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of RelaxedBernoulli distributions. The temperature should be positive.
logits – An N-D Tensor representing the log-odds of a positive event. Each entry in the Tensor parametrizes an independent RelaxedBernoulli distribution where the probability of an event is sigmoid(logits). Only one of logits or probs should be passed in.
probs – An N-D Tensor representing the probability of a positive event. Each entry in the Tensor parameterizes an independent Bernoulli distribution. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If both probs and logits are passed, or if neither.

inferpy.models.random_variable.RelaxedOneHotCategorical(*args, **kwargs)¶

Create a random variable for RelaxedOneHotCategorical.

See RelaxedOneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize RelaxedOneHotCategorical using class log-probabilities.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of RelaxedOneHotCategorical distributions. The temperature should be positive.
logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of RelaxedOneHotCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of RelaxedOneHotCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
validate_args – Unused in this distribution.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member. If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – A name for this distribution (optional).

inferpy.models.random_variable.Sample(*args, **kwargs)¶

Create a random variable for Sample.

See Sample for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the Sample distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
sample_shape – int scalar or vector Tensor representing the shape of a single sample.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
name – The name for ops managed by the distribution. Default value: None (i.e., ‘Sample’ + distribution.name).

inferpy.models.random_variable.SinhArcsinh(*args, **kwargs)¶

Create a random variable for SinhArcsinh.

See SinhArcsinh for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct SinhArcsinh distribution on (-inf, inf).

Arguments (loc, scale, skewness, tailweight) must have broadcastable shape (indexing batch dimensions). They must all have the same dtype.

Parameters

loc – Floating-point Tensor.
scale – Tensor of same dtype as loc.
skewness – Skewness parameter. Default is 0.0 (no skew).
tailweight – Tailweight parameter. Default is 1.0 (unchanged tailweight)
distribution – tf.Distribution-like instance. Distribution that is transformed to produce this distribution. Default is tfd.Normal(0., 1.). Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a SinhArcsinh sample and distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.StudentT(*args, **kwargs)¶

Create a random variable for StudentT.

See StudentT for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Student’s t distributions.

The distributions have degree of freedom df, mean loc, and scale scale.

The parameters df, loc, and scale must be shaped in a way that supports broadcasting (e.g. df + loc + scale is a valid operation).

Parameters

df – Floating-point Tensor. The degrees of freedom of the distribution(s). df must contain only positive values.
loc – Floating-point Tensor. The mean(s) of the distribution(s).
scale – Floating-point Tensor. The scaling factor(s) for the distribution(s). Note that scale is not technically the standard deviation of this distribution but has semantics more similar to standard deviation than variance.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.random_variable.StudentTProcess(*args, **kwargs)¶

Create a random variable for StudentTProcess.

See StudentTProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a StudentTProcess Distribution.

Parameters

df – Positive Floating-point Tensor representing the degrees of freedom. Must be greater than 2.
kernel – PositiveSemidefiniteKernel-like instance representing the TP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the TP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to a e-dimensional multivariate Student’s T. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
mean_fn – Python callable that acts on index_points to produce a (batch of) vector(s) of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies constant zero function.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “StudentTProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.random_variable.TransformedDistribution(*args, **kwargs)¶

Create a random variable for TransformedDistribution.

See TransformedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Transformed Distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
bijector – The object responsible for calculating the transformation. Typically an instance of Bijector.
batch_shape – integer vector Tensor which overrides distribution batch_shape; valid only if distribution.is_scalar_batch().
event_shape – integer vector Tensor which overrides distribution event_shape; valid only if distribution.is_scalar_event().
kwargs_split_fn –
Python callable which takes a kwargs dict and returns a tuple of kwargs dict`s for each of the `distribution and bijector parameters respectively. Default value: _default_kwargs_split_fn (i.e.,

`lambda kwargs: (kwargs.get(‘distribution_kwargs’, {}),
kwargs.get(‘bijector_kwargs’, {}))`)
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
parameters – Locals dict captured by subclass constructor, to be used for copy/slice re-instantiation operations.
name – Python str name prefixed to Ops created by this class. Default: bijector.name + distribution.name.

inferpy.models.random_variable.Triangular(*args, **kwargs)¶

Create a random variable for Triangular.

See Triangular for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Triangular distributions.

Parameters

low – Floating point tensor, lower boundary of the output interval. Must have low < high. Default value: 0.
high – Floating point tensor, upper boundary of the output interval. Must have low < high. Default value: 1.
peak – Floating point tensor, mode of the output interval. Must have low <= peak and peak <= high. Default value: 0.5.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Triangular’.

Raises

InvalidArgumentError – if validate_args=True and one of the following is True: * low >= high. * peak > high. * low > peak.

inferpy.models.random_variable.TruncatedNormal(*args, **kwargs)¶

Create a random variable for TruncatedNormal.

See TruncatedNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct TruncatedNormal.

All parameters of the distribution will be broadcast to the same shape, so the resulting distribution will have a batch_shape of the broadcast shape of all parameters.

Parameters

loc – Floating point tensor; the mean of the normal distribution(s) ( note that the mean of the resulting distribution will be different since it is modified by the bounds).
scale – Floating point tensor; the std deviation of the normal distribution(s).
low – float Tensor representing lower bound of the distribution’s support. Must be such that low < high.
high – float Tensor representing upper bound of the distribution’s support. Must be such that low < high.
validate_args – Python bool, default False. When True distribution parameters are checked at run-time.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.Uniform(*args, **kwargs)¶

Create a random variable for Uniform.

See Uniform for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Uniform distributions.

Parameters

low – Floating point tensor, lower boundary of the output interval. Must have low < high.
high – Floating point tensor, upper boundary of the output interval. Must have low < high.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

InvalidArgumentError – if low >= high and validate_args=False.

inferpy.models.random_variable.VariationalGaussianProcess(*args, **kwargs)¶

Create a random variable for VariationalGaussianProcess.

See VariationalGaussianProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a VariationalGaussianProcess Distribution.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the VGP is defined. Shape has the form [b1, …, bB, e1, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e1 is the number (size) of index points in each batch (we denote it e1 to distinguish it from the numer of inducing index points, denoted e2 below). Ultimately the VariationalGaussianProcess distribution corresponds to an e1-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape, the batch shape of inducing_index_points, and any batch dims yielded by mean_fn.
inducing_index_points – float Tensor of locations of inducing points in the index set. Shape has the form [b1, …, bB, e2, f1, …, fF], just like index_points. The batch shape components needn’t be identical to those of index_points, but must be broadcast compatible with them.
variational_inducing_observations_loc – float Tensor; the mean of the (full-rank Gaussian) variational posterior over function values at the inducing points, conditional on observed data. Shape has the form [b1, …, bB, e2], where b1, …, bB is broadcast compatible with other parameters’ batch shapes, and e2 is the number of inducing points.
variational_inducing_observations_scale – float Tensor; the scale matrix of the (full-rank Gaussian) variational posterior over function values at the inducing points, conditional on observed data. Shape has the form [b1, …, bB, e2, e2], where b1, …, bB is broadcast compatible with other parameters and e2 is the number of inducing points.
mean_fn – Python callable that acts on index points to produce a (batch of) vector(s) of mean values at those index points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is (broadcastable with) [b1, …, bB]. Default value: None implies constant zero function.
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
predictive_noise_variance – float Tensor representing additional variance in the posterior predictive model. If None, we simply re-use observation_noise_variance for the posterior predictive noise. If set explicitly, however, we use the given value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “VariationalGaussianProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.random_variable.VectorDeterministic(*args, **kwargs)¶

Create a random variable for VectorDeterministic.

See VectorDeterministic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a VectorDeterministic distribution on R^k, for k >= 0.

Note that there is only one point in R^0, the “point” []. So if k = 0 then self.prob([]) == 1.

The atol and rtol parameters allow for some slack in pmf computations, e.g. due to floating-point error.

``` pmf(x; loc)

```

Parameters

loc – Numeric Tensor of shape [B1, …, Bb, k], with b >= 0, k >= 0 The point (or batch of points) on which this distribution is supported.
atol – Non-negative Tensor of same dtype as loc and broadcastable shape. The absolute tolerance for comparing closeness to loc. Default is 0.
rtol – Non-negative Tensor of same dtype as loc and broadcastable shape. The relative tolerance for comparing closeness to loc. Default is 0.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.random_variable.VectorDiffeomixture(*args, **kwargs)¶

Create a random variable for VectorDiffeomixture.

See VectorDiffeomixture for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the VectorDiffeomixture on R^d.

The vector diffeomixture (VDM) approximates the compound distribution

`none p(x) = int p(x | z) p(z) dz, where z is in the K-simplex, and p(x | z) := p(x | loc=sum_k z[k] loc[k], scale=sum_k z[k] scale[k]) `

Parameters

mix_loc – float-like Tensor with shape [b1, …, bB, K-1]. In terms of samples, larger mix_loc[…, k] ==> Z is more likely to put more weight on its kth component.
temperature – float-like Tensor. Broadcastable with mix_loc. In terms of samples, smaller temperature means one component is more likely to dominate. I.e., smaller temperature makes the VDM look more like a standard mixture of K components.
distribution – tfp.distributions.Distribution-like instance. Distribution from which d iid samples are used as input to the selected affine transformation. Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a VectorDiffeomixture sample and the distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
loc – Length-K list of float-type Tensor`s. The `k-th element represents the shift used for the k-th affine transformation. If the k-th item is None, loc is implicitly 0. When specified, must have shape [B1, …, Bb, d] where b >= 0 and d is the event size.
scale – Length-K list of LinearOperator`s. Each should be positive-definite and operate on a `d-dimensional vector space. The k-th element represents the scale used for the k-th affine transformation. LinearOperator`s must have shape `[B1, …, Bb, d, d], b >= 0, i.e., characterizes b-batches of d x d matrices
quadrature_size – Python int scalar representing number of quadrature points. Larger quadrature_size means q_N(x) better approximates p(x).
quadrature_fn – Python callable taking normal_loc, normal_scale, quadrature_size, validate_args and returning tuple(grid, probs) representing the SoftmaxNormal grid and corresponding normalized weight. normalized) weight. Default value: quadrature_scheme_softmaxnormal_quantiles.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if not scale or len(scale) < 2.
ValueError – if len(loc) != len(scale)
ValueError – if quadrature_grid_and_probs is not None and len(quadrature_grid_and_probs[0]) != len(quadrature_grid_and_probs[1])
ValueError – if validate_args and any not scale.is_positive_definite.
TypeError – if any scale.dtype != scale[0].dtype.
TypeError – if any loc.dtype != scale[0].dtype.
NotImplementedError – if len(scale) != 2.
ValueError – if not distribution.is_scalar_batch.
ValueError – if not distribution.is_scalar_event.

inferpy.models.random_variable.VectorExponentialDiag(*args, **kwargs)¶

Create a random variable for VectorExponentialDiag.

See VectorExponentialDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Vector Exponential distribution supported on a subset of R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T.

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.random_variable.VectorLaplaceDiag(*args, **kwargs)¶

Create a random variable for VectorLaplaceDiag.

See VectorLaplaceDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Vector Laplace distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = 2 * scale @ scale.T.

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.random_variable.VectorSinhArcsinhDiag(*args, **kwargs)¶

Create a random variable for VectorSinhArcsinhDiag.

See VectorSinhArcsinhDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct VectorSinhArcsinhDiag distribution on R^k.

The arguments scale_diag and scale_identity_multiplier combine to define the diagonal scale referred to in this class docstring:

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scale-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scale k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
skewness – Skewness parameter. floating-point Tensor with shape broadcastable with event_shape.
tailweight – Tailweight parameter. floating-point Tensor with shape broadcastable with event_shape.
distribution – tf.Distribution-like instance. Distribution from which k iid samples are used as input to transformation F. Default is tfd.Normal(loc=0., scale=1.). Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a VectorSinhArcsinhDiag sample and distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.random_variable.VonMises(*args, **kwargs)¶

Create a random variable for VonMises.

See VonMises for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct von Mises distributions with given location and concentration.

The parameters loc and concentration must be shaped in a way that supports broadcasting (e.g. loc + concentration is a valid operation).

Parameters

loc – Floating point tensor, the circular means of the distribution(s).
concentration – Floating point tensor, the level of concentration of the distribution(s) around loc. Must take non-negative values. concentration = 0 defines a Uniform distribution, while concentration = +inf indicates a Deterministic distribution at loc.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and concentration are different dtypes.

inferpy.models.random_variable.VonMisesFisher(*args, **kwargs)¶

Create a random variable for VonMisesFisher.

See VonMisesFisher for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Creates a new VonMisesFisher instance.

Parameters

mean_direction – Floating-point Tensor with shape [B1, … Bn, D]. A unit vector indicating the mode of the distribution, or the unit-normalized direction of the mean. (This is not in general the mean of the distribution; the mean is not generally in the support of the distribution.) NOTE: D is currently restricted to <= 5.
concentration – Floating-point Tensor having batch shape [B1, … Bn] broadcastable with mean_direction. The level of concentration of samples around the mean_direction. concentration=0 indicates a uniform distribution over the unit hypersphere, and concentration=+inf indicates a Deterministic distribution (delta function) at mean_direction.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – For known-bad arguments, i.e. unsupported event dimension.

inferpy.models.random_variable.Wishart(*args, **kwargs)¶

Create a random variable for Wishart.

See Wishart for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Wishart distributions.

Parameters

df – float or double Tensor. Degrees of freedom, must be greater than or equal to dimension of the scale matrix.
scale – float or double Tensor. The symmetric positive definite scale matrix of the distribution. Exactly one of scale and ‘scale_tril` must be passed.
scale_tril – float or double Tensor. The Cholesky factorization of the symmetric positive definite scale matrix of the distribution. Exactly one of scale and ‘scale_tril` must be passed.
input_output_cholesky – Python bool. If True, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is True, input to log_prob is presumed of Cholesky form and output from sample, mean, and mode are of Cholesky form. Setting this argument to True is purely a computational optimization and does not change the underlying distribution; for instance, mean returns the Cholesky of the mean, not the mean of Cholesky factors. The variance and stddev methods are unaffected by this flag. Default value: False (i.e., input/output does not have Cholesky semantics).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if zero or both of ‘scale’ and ‘scale_tril’ are passed in.

inferpy.models.random_variable.Zipf(*args, **kwargs)¶

Create a random variable for Zipf.

See Zipf for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Zipf distributions.

Parameters

power – Float like Tensor representing the power parameter. Must be strictly greater than 1.
dtype – The dtype of Tensor returned by sample. Default value: tf.int32.
interpolate_nondiscrete – Python bool. When False, log_prob returns -inf (and prob returns 0) for non-integer inputs. When True, log_prob evaluates the continuous function -power log(k) - log(zeta(power)) , which matches the Zipf pmf at integer arguments k (note that this function is not itself a normalized probability log-density). Default value: True.
sample_maximum_iterations – Maximum number of iterations of allowable iterations in sample. When validate_args=True, samples which fail to reach convergence (subject to this cap) are masked out with self.dtype.min or nan depending on self.dtype.is_integer. Default value: 100.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: ‘Zipf’.

Raises

TypeError – if power is not float like.

Module contents¶

inferpy.models.datamodel(size=None)[source]¶: This context is used to declare a plateau model. Random Variables and Parameters will use a sample_shape defined by the argument size, or by the data_model.fit. If size is not specify, the default size 1, or the size specified by fit will be used.

class inferpy.models.Parameter(initial_value, name=None)[source]¶

Bases: object

Random Variable parameter which can be optimized by an inference mechanism.

inferpy.models.probmodel(builder)[source]¶: Decorator to create probabilistic models. The function decorated must be a function which declares the Random Variables in the model. It is not needed that the function returns such variables (we capture them using ed.tape).

inferpy.models.Autoregressive(*args, **kwargs)¶

Create a random variable for Autoregressive.

See Autoregressive for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct an Autoregressive distribution.

Parameters

distribution_fn – Python callable which constructs a tfd.Distribution-like instance from a Tensor (e.g., sample0). The function must respect the “autoregressive property”, i.e., there exists a permutation of event such that each coordinate is a diffeomorphic function of on preceding coordinates.
sample0 – Initial input to distribution_fn; used to build the distribution in __init__ which in turn specifies this distribution’s properties, e.g., event_shape, batch_shape, dtype. If unspecified, then distribution_fn should be default constructable.
num_steps – Number of times distribution_fn is composed from samples, e.g., num_steps=2 implies distribution_fn(distribution_fn(sample0).sample(n)).sample().
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class. Default value: “Autoregressive”.

Raises

ValueError – if num_steps and num_elements(distribution_fn(sample0).event_shape) are both None.
ValueError – if num_steps < 1.

inferpy.models.BatchReshape(*args, **kwargs)¶

Create a random variable for BatchReshape.

See BatchReshape for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct BatchReshape distribution.

Parameters

distribution – The base distribution instance to reshape. Typically an instance of Distribution.
batch_shape – Positive int-like vector-shaped Tensor representing the new shape of the batch dimensions. Up to one dimension may contain -1, meaning the remainder of the batch size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – The name to give Ops created by the initializer. Default value: “BatchReshape” + distribution.name.

Raises

ValueError – if batch_shape is not a vector.
ValueError – if batch_shape has non-positive elements.
ValueError – if batch_shape size is not the same as a distribution.batch_shape size.

inferpy.models.Bernoulli(*args, **kwargs)¶

Create a random variable for Bernoulli.

See Bernoulli for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Bernoulli distributions.

Parameters

logits – An N-D Tensor representing the log-odds of a 1 event. Each entry in the Tensor parametrizes an independent Bernoulli distribution where the probability of an event is sigmoid(logits). Only one of logits or probs should be passed in.
probs – An N-D Tensor representing the probability of a 1 event. Each entry in the Tensor parameterizes an independent Bernoulli distribution. Only one of logits or probs should be passed in.
dtype – The type of the event samples. Default: int32.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If p and logits are passed, or if neither are passed.

inferpy.models.Beta(*args, **kwargs)¶

Create a random variable for Beta.

See Beta for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Beta distributions.

Parameters

concentration1 – Positive floating-point Tensor indicating mean number of successes; aka “alpha”. Implies self.dtype and self.batch_shape, i.e., concentration1.shape = [N1, N2, …, Nm] = self.batch_shape.
concentration0 – Positive floating-point Tensor indicating mean number of failures; aka “beta”. Otherwise has same semantics as concentration1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Binomial(*args, **kwargs)¶

Create a random variable for Binomial.

See Binomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Binomial distributions.

Parameters

total_count – Non-negative floating point tensor with shape broadcastable to [N1,…, Nm] with m >= 0 and the same dtype as probs or logits. Defines this as a batch of N1 x … x Nm different Binomial distributions. Its components should be equal to integer values.
logits – Floating point tensor representing the log-odds of a positive event with shape broadcastable to [N1,…, Nm] m >= 0, and the same dtype as total_count. Each entry represents logits for the probability of success for independent Binomial distributions. Only one of logits or probs should be passed in.
probs – Positive floating point tensor with shape broadcastable to [N1,…, Nm] m >= 0, probs in [0, 1]. Each entry represents the probability of success for independent Binomial distributions. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Blockwise(*args, **kwargs)¶

Create a random variable for Blockwise.

See Blockwise for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the Blockwise distribution.

Parameters

distributions – Python list of tfp.distributions.Distribution instances. All distribution instances must have the same batch_shape and all must have event_ndims==1, i.e., be vector-variate distributions.
dtype_override – samples of distributions will be cast to this dtype. If unspecified, all distributions must have the same dtype. Default value: None (i.e., do not cast).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Categorical(*args, **kwargs)¶

Create a random variable for Categorical.

See Categorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize Categorical distributions using class log-probabilities.

Parameters

logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
dtype – The type of the event samples (default: int32).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Cauchy(*args, **kwargs)¶

Create a random variable for Cauchy.

See Cauchy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Cauchy distributions.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor; the modes of the distribution(s).
scale – Floating point tensor; the locations of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.Chi(*args, **kwargs)¶

Create a random variable for Chi.

See Chi for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Chi distributions with parameter df.

Parameters

df – Floating point tensor, the degrees of freedom of the distribution(s). df must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class. Default value: ‘Chi’.

inferpy.models.Chi2(*args, **kwargs)¶

Create a random variable for Chi2.

See Chi2 for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Chi2 distributions with parameter df.

Parameters

df – Floating point tensor, the degrees of freedom of the distribution(s). df must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Chi2WithAbsDf(*args, **kwargs)¶

Create a random variable for Chi2WithAbsDf.

See Chi2WithAbsDf for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

DEPRECATED FUNCTION

Warning: THIS FUNCTION IS DEPRECATED. It will be removed after 2019-06-05. Instructions for updating: Chi2WithAbsDf is deprecated, use Chi2(df=tf.floor(tf.abs(df))) instead.

inferpy.models.Deterministic(*args, **kwargs)¶

Create a random variable for Deterministic.

See Deterministic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a scalar Deterministic distribution.

The atol and rtol parameters allow for some slack in pmf, cdf computations, e.g. due to floating-point error.

``` pmf(x; loc)

```

Parameters

loc – Numeric Tensor of shape [B1, …, Bb], with b >= 0. The point (or batch of points) on which this distribution is supported.
atol – Non-negative Tensor of same dtype as loc and broadcastable shape. The absolute tolerance for comparing closeness to loc. Default is 0.
rtol – Non-negative Tensor of same dtype as loc and broadcastable shape. The relative tolerance for comparing closeness to loc. Default is 0.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.VectorDeterministic(*args, **kwargs)¶

Create a random variable for VectorDeterministic.

See VectorDeterministic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a VectorDeterministic distribution on R^k, for k >= 0.

Note that there is only one point in R^0, the “point” []. So if k = 0 then self.prob([]) == 1.

The atol and rtol parameters allow for some slack in pmf computations, e.g. due to floating-point error.

``` pmf(x; loc)

```

Parameters

loc – Numeric Tensor of shape [B1, …, Bb, k], with b >= 0, k >= 0 The point (or batch of points) on which this distribution is supported.
atol – Non-negative Tensor of same dtype as loc and broadcastable shape. The absolute tolerance for comparing closeness to loc. Default is 0.
rtol – Non-negative Tensor of same dtype as loc and broadcastable shape. The relative tolerance for comparing closeness to loc. Default is 0.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Dirichlet(*args, **kwargs)¶

Create a random variable for Dirichlet.

See Dirichlet for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Dirichlet distributions.

Parameters

concentration – Positive floating-point Tensor indicating mean number of class occurrences; aka “alpha”. Implies self.dtype, and self.batch_shape, self.event_shape, i.e., if concentration.shape = [N1, N2, …, Nm, k] then batch_shape = [N1, N2, …, Nm] and event_shape = [k].
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.DirichletMultinomial(*args, **kwargs)¶

Create a random variable for DirichletMultinomial.

See DirichletMultinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of DirichletMultinomial distributions.

Parameters

total_count – Non-negative floating point tensor, whose dtype is the same as concentration. The shape is broadcastable to [N1,…, Nm] with m >= 0. Defines this as a batch of N1 x … x Nm different Dirichlet multinomial distributions. Its components should be equal to integer values.
concentration – Positive floating point tensor, whose dtype is the same as n with shape broadcastable to [N1,…, Nm, K] m >= 0. Defines this as a batch of N1 x … x Nm different K class Dirichlet multinomial distributions.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.ConditionalDistribution(*args, **kwargs)¶

Create a random variable for ConditionalDistribution.

See ConditionalDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.Distribution(*args, **kwargs)¶

Create a random variable for Distribution.

See Distribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.Empirical(*args, **kwargs)¶

Create a random variable for Empirical.

See Empirical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize Empirical distributions.

Parameters

samples – Numeric Tensor of shape [B1, …, Bk, S, E1, …, En]`, k, n >= 0. Samples or batches of samples on which the distribution is based. The first k dimensions index into a batch of independent distributions. Length of S dimension determines number of samples in each multiset. The last n dimension represents samples for each distribution. n is specified by argument event_ndims.
event_ndims – Python int32, default 0. number of dimensions for each event. When 0 this distribution has scalar samples. When 1 this distribution has vector-like samples.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if the rank of samples < event_ndims + 1.

inferpy.models.Exponential(*args, **kwargs)¶

Create a random variable for Exponential.

See Exponential for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Exponential distribution with parameter rate.

Parameters

rate – Floating point tensor, equivalent to 1 / mean. Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.FiniteDiscrete(*args, **kwargs)¶

Create a random variable for FiniteDiscrete.

See FiniteDiscrete for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a finite discrete contribution.

Parameters

outcomes – A 1-D floating or integer Tensor, representing a list of possible outcomes in strictly ascending order.
logits – A floating N-D Tensor, N >= 1, representing the log probabilities of a set of FiniteDiscrete distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each discrete value. Only one of logits or probs should be passed in.
probs – A floating N-D Tensor, N >= 1, representing the probabilities of a set of FiniteDiscrete distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each discrete value. Only one of logits or probs should be passed in.
rtol – Tensor with same dtype as outcomes. The relative tolerance for floating number comparison. Only effective when outcomes is a floating Tensor. Default is 10 * eps.
atol – Tensor with same dtype as outcomes. The absolute tolerance for floating number comparison. Only effective when outcomes is a floating Tensor. Default is 10 * eps.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value ‘NaN’ to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Gamma(*args, **kwargs)¶

Create a random variable for Gamma.

See Gamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Gamma with concentration and rate parameters.

The parameters concentration and rate must be shaped in a way that supports broadcasting (e.g. concentration + rate is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
rate – Floating point tensor, the inverse scale params of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and rate are different dtypes.

inferpy.models.GammaGamma(*args, **kwargs)¶

Create a random variable for GammaGamma.

See GammaGamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initializes a batch of Gamma-Gamma distributions.

The parameters concentration and rate must be shaped in a way that supports broadcasting (e.g. concentration + mixing_concentration + mixing_rate is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
mixing_concentration – Floating point tensor, the concentration params of the mixing Gamma distribution(s). Must contain only positive values.
mixing_rate – Floating point tensor, the rate params of the mixing Gamma distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and rate are different dtypes.

inferpy.models.GaussianProcess(*args, **kwargs)¶

Create a random variable for GaussianProcess.

See GaussianProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a GaussianProcess Distribution.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the GP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to a e-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
mean_fn – Python callable that acts on index_points to produce a (batch of) vector(s) of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies constant zero function.
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “GaussianProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.GaussianProcessRegressionModel(*args, **kwargs)¶

Create a random variable for GaussianProcessRegressionModel.

See GaussianProcessRegressionModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a GaussianProcessRegressionModel instance.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite collection, or batch of collections, of points in the index set over which the GP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to an e-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
observation_index_points – float Tensor representing finite collection, or batch of collections, of points in the index set for which some data has been observed. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims, and e is the number (size) of index points in each batch. [b1, …, bB, e] must be broadcastable with the shape of observations, and [b1, …, bB] must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc). The default value is None, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance predictive_noise_variance).
observations – float Tensor representing collection, or batch of collections, of observations corresponding to observation_index_points. Shape has the form [b1, …, bB, e], which must be brodcastable with the batch and example shapes of observation_index_points. The batch shape [b1, …, bB] must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). The default value is None, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance predictive_noise_variance).
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
predictive_noise_variance – float Tensor representing the variance in the posterior predictive model. If None, we simply re-use observation_noise_variance for the posterior predictive noise. If set explicitly, however, we use this value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
mean_fn – Python callable that acts on index_points to produce a collection, or batch of collections, of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies the constant zero function.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: ‘GaussianProcessRegressionModel’.

Raises

ValueError – if either - only one of observations and observation_index_points is given, or - mean_fn is not None and not callable.

inferpy.models.Geometric(*args, **kwargs)¶

Create a random variable for Geometric.

See Geometric for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Geometric distributions.

Parameters

logits – Floating-point Tensor with shape [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents logits for the probability of success for independent Geometric distributions and must be in the range (-inf, inf]. Only one of logits or probs should be specified.
probs – Positive floating-point Tensor with shape [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents the probability of success for independent Geometric distributions and must be in the range (0, 1]. Only one of logits or probs should be specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Gumbel(*args, **kwargs)¶

Create a random variable for Gumbel.

See Gumbel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Gumbel distributions with location and scale loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor, the means of the distribution(s).
scale – Floating point tensor, the scales of the distribution(s). scale must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Gumbel’.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.HalfCauchy(*args, **kwargs)¶

Create a random variable for HalfCauchy.

See HalfCauchy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a half-Cauchy distribution with loc and scale.

Parameters

loc – Floating-point Tensor; the location(s) of the distribution(s).
scale – Floating-point Tensor; the scale(s) of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘HalfCauchy’.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.HalfNormal(*args, **kwargs)¶

Create a random variable for HalfNormal.

See HalfNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct HalfNormals with scale scale.

Parameters

scale – Floating point tensor; the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.HiddenMarkovModel(*args, **kwargs)¶

Create a random variable for HiddenMarkovModel.

See HiddenMarkovModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize hidden Markov model.

Parameters

initial_distribution – A Categorical-like instance. Determines probability of first hidden state in Markov chain. The number of categories must match the number of categories of transition_distribution as well as both the rightmost batch dimension of transition_distribution and the rightmost batch dimension of observation_distribution.
transition_distribution – A Categorical-like instance. The rightmost batch dimension indexes the probability distribution of each hidden state conditioned on the previous hidden state.
observation_distribution – A tfp.distributions.Distribution-like instance. The rightmost batch dimension indexes the distribution of each observation conditioned on the corresponding hidden state.
num_steps – The number of steps taken in Markov chain. A python int.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: “HiddenMarkovModel”.

Raises

ValueError – if num_steps is not at least 1.
ValueError – if initial_distribution does not have scalar event_shape.
ValueError – if transition_distribution does not have scalar event_shape.
ValueError – if transition_distribution and observation_distribution are fully defined but don’t have matching rightmost dimension.

inferpy.models.Horseshoe(*args, **kwargs)¶

Create a random variable for Horseshoe.

See Horseshoe for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Horseshoe distribution with scale.

Parameters

scale – Floating point tensor; the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e., do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Horseshoe’.

inferpy.models.Independent(*args, **kwargs)¶

Create a random variable for Independent.

See Independent for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Independent distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
reinterpreted_batch_ndims – Scalar, integer number of rightmost batch dims which will be regarded as event dims. When None all but the first batch axis (batch axis 0) will be transferred to event dimensions (analogous to tf.layers.flatten).
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
name – The name for ops managed by the distribution. Default value: Independent + distribution.name.

Raises

ValueError – if reinterpreted_batch_ndims exceeds distribution.batch_ndims

inferpy.models.InverseGamma(*args, **kwargs)¶

Create a random variable for InverseGamma.

See InverseGamma for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct InverseGamma with concentration and scale parameters. (deprecated arguments)

Warning: SOME ARGUMENTS ARE DEPRECATED: (rate). They will be removed after 2019-05-08. Instructions for updating: The rate parameter is deprecated. Use scale instead.The rate parameter was always interpreted as a scale parameter, but erroneously misnamed.

The parameters concentration and scale must be shaped in a way that supports broadcasting (e.g. concentration + scale is a valid operation).

Parameters

concentration – Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
scale – Floating point tensor, the scale params of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
rate – Deprecated (mis-named) alias for scale.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if concentration and scale are different dtypes.

inferpy.models.InverseGaussian(*args, **kwargs)¶

Create a random variable for InverseGaussian.

See InverseGaussian for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs inverse Gaussian distribution with loc and concentration.

Parameters

loc – Floating-point Tensor, the loc params. Must contain only positive values.
concentration – Floating-point Tensor, the concentration params. Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘InverseGaussian’.

inferpy.models.JointDistribution(*args, **kwargs)¶

Create a random variable for JointDistribution.

See JointDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the Distribution.

This is a private method for subclass use.

Parameters

dtype – The type of the event samples. None implies no type-enforcement.
reparameterization_type – Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If tfd.NOT_REPARAMETERIZED, then no such reparameterization is available.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
parameters – Python dict of parameters used to instantiate this Distribution.
graph_parents – Python list of graph prerequisites of this Distribution.
name – Python str name prefixed to Ops created by this class. Default: subclass name.

Raises

ValueError – if any member of graph_parents is None or not a Tensor.

inferpy.models.JointDistributionCoroutine(*args, **kwargs)¶

Create a random variable for JointDistributionCoroutine.

See JointDistributionCoroutine for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionCoroutine distribution.

Parameters

model – A generator that yields a sequence of tfd.Distribution-like instances.
sample_dtype – Samples from this distribution will be structured like tf.nest.pack_sequence_as(sample_dtype, list_). sample_dtype is only used for tf.nest.pack_sequence_as structuring of outputs, never casting (which is the responsibility of the component distributions). Default value: None (i.e., tuple).
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionCoroutine”).

inferpy.models.JointDistributionNamed(*args, **kwargs)¶

Create a random variable for JointDistributionNamed.

See JointDistributionNamed for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionNamed distribution.

Parameters

model – Python dict or namedtuple of distribution-making functions each with required args corresponding only to other keys.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionNamed”).

inferpy.models.JointDistributionSequential(*args, **kwargs)¶

Create a random variable for JointDistributionSequential.

See JointDistributionSequential for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the JointDistributionSequential distribution.

Parameters

model – Python list of either tfd.Distribution instances and/or lambda functions which take the k previous distributions and returns a new tfd.Distribution instance.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False.
name – The name for ops managed by the distribution. Default value: None (i.e., “JointDistributionSequential”).

inferpy.models.Kumaraswamy(*args, **kwargs)¶

Create a random variable for Kumaraswamy.

See Kumaraswamy for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Kumaraswamy distributions.

Parameters

concentration1 – Positive floating-point Tensor indicating mean number of successes; aka “alpha”. Implies self.dtype and self.batch_shape, i.e., concentration1.shape = [N1, N2, …, Nm] = self.batch_shape.
concentration0 – Positive floating-point Tensor indicating mean number of failures; aka “beta”. Otherwise has same semantics as concentration1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Laplace(*args, **kwargs)¶

Create a random variable for Laplace.

See Laplace for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Laplace distribution with parameters loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g., loc / scale is a valid operation).

Parameters

loc – Floating point tensor which characterizes the location (center) of the distribution.
scale – Positive floating point tensor which characterizes the spread of the distribution.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale are of different dtype.

inferpy.models.LinearGaussianStateSpaceModel(*args, **kwargs)¶

Create a random variable for LinearGaussianStateSpaceModel.

See LinearGaussianStateSpaceModel for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a `LinearGaussianStateSpaceModel.

Parameters

num_timesteps – Integer Tensor total number of timesteps.
transition_matrix – A transition operator, represented by a Tensor or LinearOperator of shape [latent_size, latent_size], or by a callable taking as argument a scalar integer Tensor t and returning a Tensor or LinearOperator representing the transition operator from latent state at time t to time t + 1.
transition_noise – An instance of tfd.MultivariateNormalLinearOperator with event shape [latent_size], representing the mean and covariance of the transition noise model, or a callable taking as argument a scalar integer Tensor t and returning such a distribution representing the noise in the transition from time t to time t + 1.
observation_matrix – An observation operator, represented by a Tensor or LinearOperator of shape [observation_size, latent_size], or by a callable taking as argument a scalar integer Tensor t and returning a timestep-specific Tensor or LinearOperator.
observation_noise – An instance of tfd.MultivariateNormalLinearOperator with event shape [observation_size], representing the mean and covariance of the observation noise model, or a callable taking as argument a scalar integer Tensor t and returning a timestep-specific noise model.
initial_state_prior – An instance of MultivariateNormalLinearOperator representing the prior distribution on latent states; must have event shape [latent_size].
initial_step – optional int specifying the time of the first modeled timestep. This is added as an offset when passing timesteps t to (optional) callables specifying timestep-specific transition and observation models.
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

inferpy.models.LKJ(*args, **kwargs)¶

Create a random variable for LKJ.

See LKJ for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct LKJ distributions.

Parameters

dimension – Python int. The dimension of the correlation matrices to sample.
concentration – float or double Tensor. The positive concentration parameter of the LKJ distributions. The pdf of a sample matrix X is proportional to det(X) ** (concentration - 1).
input_output_cholesky – Python bool. If True, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is True, input to log_prob is presumed of Cholesky form and output from sample is of Cholesky form. Setting this argument to True is purely a computational optimization and does not change the underlying distribution. Additionally, validation checks which are only defined on the multiplied-out form are omitted, even if validate_args is True. Default value: False (i.e., input/output does not have Cholesky semantics).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If dimension is negative.

inferpy.models.Logistic(*args, **kwargs)¶

Create a random variable for Logistic.

See Logistic for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Logistic distributions with mean and scale loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor, the means of the distribution(s).
scale – Floating point tensor, the scales of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – The name to give Ops created by the initializer.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.LogNormal(*args, **kwargs)¶

Create a random variable for LogNormal.

See LogNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a log-normal distribution.

The LogNormal distribution models positive-valued random variables whose logarithm is normally distributed with mean loc and standard deviation scale. It is constructed as the exponential transformation of a Normal distribution.

Parameters

loc – Floating-point Tensor; the means of the underlying Normal distribution(s).
scale – Floating-point Tensor; the stddevs of the underlying Normal distribution(s).
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

inferpy.models.Mixture(*args, **kwargs)¶

Create a random variable for Mixture.

See Mixture for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a Mixture distribution.

A Mixture is defined by a Categorical (cat, representing the mixture probabilities) and a list of Distribution objects all having matching dtype, batch shape, event shape, and continuity properties (the components).

The num_classes of cat must be possible to infer at graph construction time and match len(components).

Parameters

cat – A Categorical distribution instance, representing the probabilities of distributions.
components – A list or tuple of Distribution instances. Each instance must have the same type, be defined on the same domain, and have matching event_shape and batch_shape.
validate_args – Python bool, default False. If True, raise a runtime error if batch or event ranks are inconsistent between cat and any of the distributions. This is only checked if the ranks cannot be determined statically at graph construction time.
allow_nan_stats –
Boolean, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any

batch member. If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
use_static_graph – Calls to sample will not rely on dynamic tensor indexing, allowing for some static graph compilation optimizations, but at the expense of sampling all underlying distributions in the mixture. (Possibly useful when running on TPUs). Default value: False (i.e., use dynamic indexing).
name – A name for this distribution (optional).

Raises

TypeError – If cat is not a Categorical, or components is not a list or tuple, or the elements of components are not instances of Distribution, or do not have matching dtype.
ValueError – If components is an empty list or tuple, or its elements do not have a statically known event rank. If cat.num_classes cannot be inferred at graph creation time, or the constant value of cat.num_classes is not equal to len(components), or all components and cat do not have matching static batch shapes, or all components do not have matching static event shapes.

inferpy.models.MixtureSameFamily(*args, **kwargs)¶

Create a random variable for MixtureSameFamily.

See MixtureSameFamily for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a MixtureSameFamily distribution.

Parameters

mixture_distribution – tfp.distributions.Categorical-like instance. Manages the probability of selecting components. The number of categories must match the rightmost batch dimension of the components_distribution. Must have either scalar batch_shape or batch_shape matching components_distribution.batch_shape[:-1].
components_distribution – tfp.distributions.Distribution-like instance. Right-most batch dimension indexes components.
reparameterize –
Python bool, default False. Whether to reparameterize samples of the distribution using implicit reparameterization gradients [(Figurnov et al., 2018)][1]. The gradients for the mixture logits are equivalent to the ones described by [(Graves, 2016)][2]. The gradients for the components parameters are also computed using implicit reparameterization (as opposed to ancestral sampling), meaning that all components are updated every step. Only works when:
1. components_distribution is fully reparameterized;
(2) components_distribution is either a scalar distribution or fully factorized (tfd.Independent applied to a scalar distribution); (3) batch shape has a known rank.
Experimental, may be slow and produce infs/NaNs.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if not dtype_util.is_integer(mixture_distribution.dtype).
ValueError – if mixture_distribution does not have scalar event_shape.
ValueError – if mixture_distribution.batch_shape and components_distribution.batch_shape[:-1] are both fully defined and the former is neither scalar nor equal to the latter.
ValueError – if mixture_distribution categories does not equal components_distribution rightmost batch shape.

#### References

[1]: Michael Figurnov, Shakir Mohamed and Andriy Mnih. Implicit: reparameterization gradients. In _Neural Information Processing Systems_, 2018. https://arxiv.org/abs/1805.08498
[2]: Alex Graves. Stochastic Backpropagation through Mixture Density: Distributions. _arXiv_, 2016. https://arxiv.org/abs/1607.05690

inferpy.models.Multinomial(*args, **kwargs)¶

Create a random variable for Multinomial.

See Multinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Multinomial distributions.

Parameters

total_count – Non-negative floating point tensor with shape broadcastable to [N1,…, Nm] with m >= 0. Defines this as a batch of N1 x … x Nm different Multinomial distributions. Its components should be equal to integer values.
logits – Floating point tensor representing unnormalized log-probabilities of a positive event with shape broadcastable to [N1,…, Nm, K] m >= 0, and the same dtype as total_count. Defines this as a batch of N1 x … x Nm different K class Multinomial distributions. Only one of logits or probs should be passed in.
probs – Positive floating point tensor with shape broadcastable to [N1,…, Nm, K] m >= 0 and same dtype as total_count. Defines this as a batch of N1 x … x Nm different K class Multinomial distributions. probs’s components in the last portion of its shape should sum to 1. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.MultivariateStudentTLinearOperator(*args, **kwargs)¶

Create a random variable for MultivariateStudentTLinearOperator.

See MultivariateStudentTLinearOperator for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Student’s t-distribution on R^k.

The batch_shape is the broadcast shape between df, loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc must broadcast with this.

Additional leading dimensions (if any) will index batches.

Parameters

df – A positive floating-point Tensor. Has shape [B1, …, Bb] where b >= 0.
loc – Floating-point Tensor. Has shape [B1, …, Bb, k] where k is the event size.
scale – Instance of LinearOperator with a floating dtype and shape [B1, …, Bb, k, k].
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/variance/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

Raises

TypeError – if not scale.dtype.is_floating.
ValueError – if not scale.is_positive_definite.

inferpy.models.MultivariateNormalDiag(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiag.

See MultivariateNormalDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.MultivariateNormalDiagWithSoftplusScale(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiagWithSoftplusScale.

See MultivariateNormalDiagWithSoftplusScale for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

DEPRECATED FUNCTION

Warning: THIS FUNCTION IS DEPRECATED. It will be removed after 2019-06-05. Instructions for updating: MultivariateNormalDiagWithSoftplusScale is deprecated, use MultivariateNormalDiag(loc=loc, scale_diag=tf.nn.softplus(scale_diag)) instead.

inferpy.models.MultivariateNormalDiagPlusLowRank(*args, **kwargs)¶

Create a random variable for MultivariateNormalDiagPlusLowRank.

See MultivariateNormalDiagPlusLowRank for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

```none scale = diag(scale_diag + scale_identity_multiplier ones(k)) +

```

where:

scale_diag.shape = [k],
scale_identity_multiplier.shape = [],
scale_perturb_factor.shape = [k, r], typically k >> r, and,
scale_perturb_diag.shape = [r].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_perturb_factor – Floating-point Tensor representing a rank-r perturbation added to scale. May have shape [B1, …, Bb, k, r], b >= 0, and characterizes b-batches of rank-r updates to scale. When None, no rank-r update is added to scale.
scale_perturb_diag – Floating-point Tensor representing a diagonal matrix inside the rank-r perturbation added to scale. May have shape [B1, …, Bb, r], b >= 0, and characterizes b-batches of r x r diagonal matrices inside the perturbation added to scale. When None, an identity matrix is used inside the perturbation. Can only be specified if scale_perturb_factor is also specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.MultivariateNormalFullCovariance(*args, **kwargs)¶

Create a random variable for MultivariateNormalFullCovariance.

See MultivariateNormalFullCovariance for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and covariance_matrix arguments.

The event_shape is given by last dimension of the matrix implied by covariance_matrix. The last dimension of loc (if provided) must broadcast with this.

A non-batch covariance_matrix matrix is a k x k symmetric positive definite matrix. In other words it is (real) symmetric with all eigenvalues strictly positive.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
covariance_matrix – Floating-point, symmetric positive definite Tensor of same dtype as loc. The strict upper triangle of covariance_matrix is ignored, so if covariance_matrix is not symmetric no error will be raised (unless validate_args is True). covariance_matrix has shape [B1, …, Bb, k, k] where b >= 0 and k is the event size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if neither loc nor covariance_matrix are specified.

inferpy.models.MultivariateNormalLinearOperator(*args, **kwargs)¶

Create a random variable for MultivariateNormalLinearOperator.

See MultivariateNormalLinearOperator for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale – Instance of LinearOperator with same dtype as loc and shape [B1, …, Bb, k, k].
validate_args – Python bool, default False. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – The name to give Ops created by the initializer.

Raises

ValueError – if scale is unspecified.
TypeError – if not scale.dtype.is_floating

inferpy.models.MultivariateNormalTriL(*args, **kwargs)¶

Create a random variable for MultivariateNormalTriL.

See MultivariateNormalTriL for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Multivariate Normal distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T. A (non-batch) scale matrix is:

`none scale = scale_tril `

where scale_tril is lower-triangular k x k matrix with non-zero diagonal, i.e., tf.diag_part(scale_tril) != 0.

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_tril – Floating-point, lower-triangular Tensor with non-zero diagonal elements. scale_tril has shape [B1, …, Bb, k, k] where b >= 0 and k is the event size.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if neither loc nor scale_tril are specified.

inferpy.models.NegativeBinomial(*args, **kwargs)¶

Create a random variable for NegativeBinomial.

See NegativeBinomial for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct NegativeBinomial distributions.

Parameters

total_count – Non-negative floating-point Tensor with shape broadcastable to [B1,…, Bb] with b >= 0 and the same dtype as probs or logits. Defines this as a batch of N1 x … x Nm different Negative Binomial distributions. In practice, this represents the number of negative Bernoulli trials to stop at (the total_count of failures), but this is still a valid distribution when total_count is a non-integer.
logits – Floating-point Tensor with shape broadcastable to [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents logits for the probability of success for independent Negative Binomial distributions and must be in the open interval (-inf, inf). Only one of logits or probs should be specified.
probs – Positive floating-point Tensor with shape broadcastable to [B1, …, Bb] where b >= 0 indicates the number of batch dimensions. Each entry represents the probability of success for independent Negative Binomial distributions and must be in the open interval (0, 1). Only one of logits or probs should be specified.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Normal(*args, **kwargs)¶

Create a random variable for Normal.

See Normal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Normal distributions with mean and stddev loc and scale.

The parameters loc and scale must be shaped in a way that supports broadcasting (e.g. loc + scale is a valid operation).

Parameters

loc – Floating point tensor; the means of the distribution(s).
scale – Floating point tensor; the stddevs of the distribution(s). Must contain only positive values.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale have different dtype.

inferpy.models.OneHotCategorical(*args, **kwargs)¶

Create a random variable for OneHotCategorical.

See OneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize OneHotCategorical distributions using class log-probabilities.

Parameters

logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of Categorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
dtype – The type of the event samples (default: int32).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Pareto(*args, **kwargs)¶

Create a random variable for Pareto.

See Pareto for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Pareto distribution with concentration and scale.

Parameters

concentration – Floating point tensor. Must contain only positive values.
scale – Floating point tensor, equivalent to mode. scale also restricts the domain of this distribution to be in [scale, inf). Must contain only positive values. Default value: 1.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False (i.e. do not validate args).
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Pareto’.

inferpy.models.Poisson(*args, **kwargs)¶

Create a random variable for Poisson.

See Poisson for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Poisson distributions.

Parameters

rate – Floating point tensor, the rate parameter. rate must be positive. Must specify exactly one of rate and log_rate.
log_rate – Floating point tensor, the log of the rate parameter. Must specify exactly one of rate and log_rate.
interpolate_nondiscrete – Python bool. When False, log_prob returns -inf (and prob returns 0) for non-integer inputs. When True, log_prob evaluates the continuous function k * log_rate - lgamma(k+1) - rate, which matches the Poisson pmf at integer arguments k (note that this function is not itself a normalized probability log-density). Default value: True.
validate_args – Python bool. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if none or both of rate, log_rate are specified.
TypeError – if rate is not a float-type.
TypeError – if log_rate is not a float-type.

inferpy.models.PoissonLogNormalQuadratureCompound(*args, **kwargs)¶

Create a random variable for PoissonLogNormalQuadratureCompound.

See PoissonLogNormalQuadratureCompound for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the PoissonLogNormalQuadratureCompound`.

Note: probs returned by (optional) quadrature_fn are presumed to be either a length-quadrature_size vector or a batch of vectors in 1-to-1 correspondence with the returned grid. (I.e., broadcasting is only partially supported.)

Parameters

loc – float-like (batch of) scalar Tensor; the location parameter of the LogNormal prior.
scale – float-like (batch of) scalar Tensor; the scale parameter of the LogNormal prior.
quadrature_size – Python int scalar representing the number of quadrature points.
quadrature_fn – Python callable taking loc, scale, quadrature_size, validate_args and returning tuple(grid, probs) representing the LogNormal grid and corresponding normalized weight. normalized) weight. Default value: quadrature_scheme_lognormal_quantiles.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if quadrature_grid and quadrature_probs have different base dtype.

inferpy.models.QuantizedDistribution(*args, **kwargs)¶

Create a random variable for QuantizedDistribution.

See QuantizedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Quantized Distribution representing Y = ceiling(X).

Some properties are inherited from the distribution defining X. Example: allow_nan_stats is determined for this QuantizedDistribution by reading the distribution.

Parameters

distribution – The base distribution class to transform. Typically an instance of Distribution.
low – Tensor with same dtype as this distribution and shape able to be added to samples. Should be a whole number. Default None. If provided, base distribution’s prob should be defined at low.
high – Tensor with same dtype as this distribution and shape able to be added to samples. Should be a whole number. Default None. If provided, base distribution’s prob should be defined at high - 1. high must be strictly greater than low.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – If dist_cls is not a subclass of Distribution or continuous.
NotImplementedError – If the base distribution does not implement cdf.

inferpy.models.RelaxedBernoulli(*args, **kwargs)¶

Create a random variable for RelaxedBernoulli.

See RelaxedBernoulli for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct RelaxedBernoulli distributions.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of RelaxedBernoulli distributions. The temperature should be positive.
logits – An N-D Tensor representing the log-odds of a positive event. Each entry in the Tensor parametrizes an independent RelaxedBernoulli distribution where the probability of an event is sigmoid(logits). Only one of logits or probs should be passed in.
probs – An N-D Tensor representing the probability of a positive event. Each entry in the Tensor parameterizes an independent Bernoulli distribution. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – If both probs and logits are passed, or if neither.

inferpy.models.ExpRelaxedOneHotCategorical(*args, **kwargs)¶

Create a random variable for ExpRelaxedOneHotCategorical.

See ExpRelaxedOneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize ExpRelaxedOneHotCategorical using class log-probabilities.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of ExpRelaxedCategorical distributions. The temperature should be positive.
logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of ExpRelaxedCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of ExpRelaxedCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.RelaxedOneHotCategorical(*args, **kwargs)¶

Create a random variable for RelaxedOneHotCategorical.

See RelaxedOneHotCategorical for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize RelaxedOneHotCategorical using class log-probabilities.

Parameters

temperature – An 0-D Tensor, representing the temperature of a set of RelaxedOneHotCategorical distributions. The temperature should be positive.
logits – An N-D Tensor, N >= 1, representing the log probabilities of a set of RelaxedOneHotCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of logits for each class. Only one of logits or probs should be passed in.
probs – An N-D Tensor, N >= 1, representing the probabilities of a set of RelaxedOneHotCategorical distributions. The first N - 1 dimensions index into a batch of independent distributions and the last dimension represents a vector of probabilities for each class. Only one of logits or probs should be passed in.
validate_args – Unused in this distribution.
allow_nan_stats – Python bool, default True. If False, raise an exception if a statistic (e.g. mean/mode/etc…) is undefined for any batch member. If True, batch members with valid parameters leading to undefined statistics will return NaN for this statistic.
name – A name for this distribution (optional).

inferpy.models.Sample(*args, **kwargs)¶

Create a random variable for Sample.

See Sample for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct the Sample distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
sample_shape – int scalar or vector Tensor representing the shape of a single sample.
validate_args – Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed.
name – The name for ops managed by the distribution. Default value: None (i.e., ‘Sample’ + distribution.name).

inferpy.models.SinhArcsinh(*args, **kwargs)¶

Create a random variable for SinhArcsinh.

See SinhArcsinh for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct SinhArcsinh distribution on (-inf, inf).

Arguments (loc, scale, skewness, tailweight) must have broadcastable shape (indexing batch dimensions). They must all have the same dtype.

Parameters

loc – Floating-point Tensor.
scale – Tensor of same dtype as loc.
skewness – Skewness parameter. Default is 0.0 (no skew).
tailweight – Tailweight parameter. Default is 1.0 (unchanged tailweight)
distribution – tf.Distribution-like instance. Distribution that is transformed to produce this distribution. Default is tfd.Normal(0., 1.). Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a SinhArcsinh sample and distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.StudentT(*args, **kwargs)¶

Create a random variable for StudentT.

See StudentT for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Student’s t distributions.

The distributions have degree of freedom df, mean loc, and scale scale.

The parameters df, loc, and scale must be shaped in a way that supports broadcasting (e.g. df + loc + scale is a valid operation).

Parameters

df – Floating-point Tensor. The degrees of freedom of the distribution(s). df must contain only positive values.
loc – Floating-point Tensor. The mean(s) of the distribution(s).
scale – Floating-point Tensor. The scaling factor(s) for the distribution(s). Note that scale is not technically the standard deviation of this distribution but has semantics more similar to standard deviation than variance.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and scale are different dtypes.

inferpy.models.StudentTProcess(*args, **kwargs)¶

Create a random variable for StudentTProcess.

See StudentTProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a StudentTProcess Distribution.

Parameters

df – Positive Floating-point Tensor representing the degrees of freedom. Must be greater than 2.
kernel – PositiveSemidefiniteKernel-like instance representing the TP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the TP is defined. Shape has the form [b1, …, bB, e, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e is the number (size) of index points in each batch. Ultimately this distribution corresponds to a e-dimensional multivariate Student’s T. The batch shape must be broadcastable with kernel.batch_shape and any batch dims yielded by mean_fn.
mean_fn – Python callable that acts on index_points to produce a (batch of) vector(s) of mean values at index_points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is broadcastable with [b1, …, bB]. Default value: None implies constant zero function.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “StudentTProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.ConditionalTransformedDistribution(*args, **kwargs)¶

Create a random variable for ConditionalTransformedDistribution.

See ConditionalTransformedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Transformed Distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
bijector – The object responsible for calculating the transformation. Typically an instance of Bijector.
batch_shape – integer vector Tensor which overrides distribution batch_shape; valid only if distribution.is_scalar_batch().
event_shape – integer vector Tensor which overrides distribution event_shape; valid only if distribution.is_scalar_event().
kwargs_split_fn –
Python callable which takes a kwargs dict and returns a tuple of kwargs dict`s for each of the `distribution and bijector parameters respectively. Default value: _default_kwargs_split_fn (i.e.,

`lambda kwargs: (kwargs.get(‘distribution_kwargs’, {}),
kwargs.get(‘bijector_kwargs’, {}))`)
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
parameters – Locals dict captured by subclass constructor, to be used for copy/slice re-instantiation operations.
name – Python str name prefixed to Ops created by this class. Default: bijector.name + distribution.name.

inferpy.models.TransformedDistribution(*args, **kwargs)¶

Create a random variable for TransformedDistribution.

See TransformedDistribution for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct a Transformed Distribution.

Parameters

distribution – The base distribution instance to transform. Typically an instance of Distribution.
bijector – The object responsible for calculating the transformation. Typically an instance of Bijector.
batch_shape – integer vector Tensor which overrides distribution batch_shape; valid only if distribution.is_scalar_batch().
event_shape – integer vector Tensor which overrides distribution event_shape; valid only if distribution.is_scalar_event().
kwargs_split_fn –
Python callable which takes a kwargs dict and returns a tuple of kwargs dict`s for each of the `distribution and bijector parameters respectively. Default value: _default_kwargs_split_fn (i.e.,

`lambda kwargs: (kwargs.get(‘distribution_kwargs’, {}),
kwargs.get(‘bijector_kwargs’, {}))`)
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
parameters – Locals dict captured by subclass constructor, to be used for copy/slice re-instantiation operations.
name – Python str name prefixed to Ops created by this class. Default: bijector.name + distribution.name.

inferpy.models.Triangular(*args, **kwargs)¶

Create a random variable for Triangular.

See Triangular for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Triangular distributions.

Parameters

low – Floating point tensor, lower boundary of the output interval. Must have low < high. Default value: 0.
high – Floating point tensor, upper boundary of the output interval. Must have low < high. Default value: 1.
peak – Floating point tensor, mode of the output interval. Must have low <= peak and peak <= high. Default value: 0.5.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: True.
name – Python str name prefixed to Ops created by this class. Default value: ‘Triangular’.

Raises

InvalidArgumentError – if validate_args=True and one of the following is True: * low >= high. * peak > high. * low > peak.

inferpy.models.TruncatedNormal(*args, **kwargs)¶

Create a random variable for TruncatedNormal.

See TruncatedNormal for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct TruncatedNormal.

All parameters of the distribution will be broadcast to the same shape, so the resulting distribution will have a batch_shape of the broadcast shape of all parameters.

Parameters

loc – Floating point tensor; the mean of the normal distribution(s) ( note that the mean of the resulting distribution will be different since it is modified by the bounds).
scale – Floating point tensor; the std deviation of the normal distribution(s).
low – float Tensor representing lower bound of the distribution’s support. Must be such that low < high.
high – float Tensor representing upper bound of the distribution’s support. Must be such that low < high.
validate_args – Python bool, default False. When True distribution parameters are checked at run-time.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

inferpy.models.Uniform(*args, **kwargs)¶

Create a random variable for Uniform.

See Uniform for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Uniform distributions.

Parameters

low – Floating point tensor, lower boundary of the output interval. Must have low < high.
high – Floating point tensor, upper boundary of the output interval. Must have low < high.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

InvalidArgumentError – if low >= high and validate_args=False.

inferpy.models.VariationalGaussianProcess(*args, **kwargs)¶

Create a random variable for VariationalGaussianProcess.

See VariationalGaussianProcess for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Instantiate a VariationalGaussianProcess Distribution.

Parameters

kernel – PositiveSemidefiniteKernel-like instance representing the GP’s covariance function.
index_points – float Tensor representing finite (batch of) vector(s) of points in the index set over which the VGP is defined. Shape has the form [b1, …, bB, e1, f1, …, fF] where F is the number of feature dimensions and must equal kernel.feature_ndims and e1 is the number (size) of index points in each batch (we denote it e1 to distinguish it from the numer of inducing index points, denoted e2 below). Ultimately the VariationalGaussianProcess distribution corresponds to an e1-dimensional multivariate normal. The batch shape must be broadcastable with kernel.batch_shape, the batch shape of inducing_index_points, and any batch dims yielded by mean_fn.
inducing_index_points – float Tensor of locations of inducing points in the index set. Shape has the form [b1, …, bB, e2, f1, …, fF], just like index_points. The batch shape components needn’t be identical to those of index_points, but must be broadcast compatible with them.
variational_inducing_observations_loc – float Tensor; the mean of the (full-rank Gaussian) variational posterior over function values at the inducing points, conditional on observed data. Shape has the form [b1, …, bB, e2], where b1, …, bB is broadcast compatible with other parameters’ batch shapes, and e2 is the number of inducing points.
variational_inducing_observations_scale – float Tensor; the scale matrix of the (full-rank Gaussian) variational posterior over function values at the inducing points, conditional on observed data. Shape has the form [b1, …, bB, e2, e2], where b1, …, bB is broadcast compatible with other parameters and e2 is the number of inducing points.
mean_fn – Python callable that acts on index points to produce a (batch of) vector(s) of mean values at those index points. Takes a Tensor of shape [b1, …, bB, f1, …, fF] and returns a Tensor whose shape is (broadcastable with) [b1, …, bB]. Default value: None implies constant zero function.
observation_noise_variance – float Tensor representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (kernel.batch_shape, index_points, etc.). Default value: 0.
predictive_noise_variance – float Tensor representing additional variance in the posterior predictive model. If None, we simply re-use observation_noise_variance for the posterior predictive noise. If set explicitly, however, we use the given value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
jitter – float scalar Tensor added to the diagonal of the covariance matrix to ensure positive definiteness of the covariance matrix. Default value: 1e-6.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: “VariationalGaussianProcess”.

Raises

ValueError – if mean_fn is not None and is not callable.

inferpy.models.VectorDiffeomixture(*args, **kwargs)¶

Create a random variable for VectorDiffeomixture.

See VectorDiffeomixture for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Constructs the VectorDiffeomixture on R^d.

The vector diffeomixture (VDM) approximates the compound distribution

`none p(x) = int p(x | z) p(z) dz, where z is in the K-simplex, and p(x | z) := p(x | loc=sum_k z[k] loc[k], scale=sum_k z[k] scale[k]) `

Parameters

mix_loc – float-like Tensor with shape [b1, …, bB, K-1]. In terms of samples, larger mix_loc[…, k] ==> Z is more likely to put more weight on its kth component.
temperature – float-like Tensor. Broadcastable with mix_loc. In terms of samples, smaller temperature means one component is more likely to dominate. I.e., smaller temperature makes the VDM look more like a standard mixture of K components.
distribution – tfp.distributions.Distribution-like instance. Distribution from which d iid samples are used as input to the selected affine transformation. Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a VectorDiffeomixture sample and the distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
loc – Length-K list of float-type Tensor`s. The `k-th element represents the shift used for the k-th affine transformation. If the k-th item is None, loc is implicitly 0. When specified, must have shape [B1, …, Bb, d] where b >= 0 and d is the event size.
scale – Length-K list of LinearOperator`s. Each should be positive-definite and operate on a `d-dimensional vector space. The k-th element represents the scale used for the k-th affine transformation. LinearOperator`s must have shape `[B1, …, Bb, d, d], b >= 0, i.e., characterizes b-batches of d x d matrices
quadrature_size – Python int scalar representing number of quadrature points. Larger quadrature_size means q_N(x) better approximates p(x).
quadrature_fn – Python callable taking normal_loc, normal_scale, quadrature_size, validate_args and returning tuple(grid, probs) representing the SoftmaxNormal grid and corresponding normalized weight. normalized) weight. Default value: quadrature_scheme_softmaxnormal_quantiles.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if not scale or len(scale) < 2.
ValueError – if len(loc) != len(scale)
ValueError – if quadrature_grid_and_probs is not None and len(quadrature_grid_and_probs[0]) != len(quadrature_grid_and_probs[1])
ValueError – if validate_args and any not scale.is_positive_definite.
TypeError – if any scale.dtype != scale[0].dtype.
TypeError – if any loc.dtype != scale[0].dtype.
NotImplementedError – if len(scale) != 2.
ValueError – if not distribution.is_scalar_batch.
ValueError – if not distribution.is_scalar_event.

inferpy.models.VectorExponentialDiag(*args, **kwargs)¶

Create a random variable for VectorExponentialDiag.

See VectorExponentialDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Vector Exponential distribution supported on a subset of R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = scale @ scale.T.

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.VectorLaplaceDiag(*args, **kwargs)¶

Create a random variable for VectorLaplaceDiag.

See VectorLaplaceDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Vector Laplace distribution on R^k.

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this.

Recall that covariance = 2 * scale @ scale.T.

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

where:

scale_diag.shape = [k], and,
scale_identity_multiplier.shape = [].

Additional leading dimensions (if any) will index batches.

If both scale_diag and scale_identity_multiplier are None, then scale is the Identity matrix.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scaled-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scaled k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.VectorSinhArcsinhDiag(*args, **kwargs)¶

Create a random variable for VectorSinhArcsinhDiag.

See VectorSinhArcsinhDiag for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct VectorSinhArcsinhDiag distribution on R^k.

The arguments scale_diag and scale_identity_multiplier combine to define the diagonal scale referred to in this class docstring:

`none scale = diag(scale_diag + scale_identity_multiplier * ones(k)) `

The batch_shape is the broadcast shape between loc and scale arguments.

The event_shape is given by last dimension of the matrix implied by scale. The last dimension of loc (if provided) must broadcast with this

Additional leading dimensions (if any) will index batches.

Parameters

loc – Floating-point Tensor. If this is set to None, loc is implicitly 0. When specified, may have shape [B1, …, Bb, k] where b >= 0 and k is the event size.
scale_diag – Non-zero, floating-point Tensor representing a diagonal matrix added to scale. May have shape [B1, …, Bb, k], b >= 0, and characterizes b-batches of k x k diagonal matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
scale_identity_multiplier – Non-zero, floating-point Tensor representing a scale-identity-matrix added to scale. May have shape [B1, …, Bb], b >= 0, and characterizes b-batches of scale k x k identity matrices added to scale. When both scale_identity_multiplier and scale_diag are None then scale is the Identity.
skewness – Skewness parameter. floating-point Tensor with shape broadcastable with event_shape.
tailweight – Tailweight parameter. floating-point Tensor with shape broadcastable with event_shape.
distribution – tf.Distribution-like instance. Distribution from which k iid samples are used as input to transformation F. Default is tfd.Normal(loc=0., scale=1.). Must be a scalar-batch, scalar-event distribution. Typically distribution.reparameterization_type = FULLY_REPARAMETERIZED or it is a function of non-trainable parameters. WARNING: If you backprop through a VectorSinhArcsinhDiag sample and distribution is not FULLY_REPARAMETERIZED yet is a function of trainable variables, then the gradient will be incorrect!
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if at most scale_identity_multiplier is specified.

inferpy.models.VonMises(*args, **kwargs)¶

Create a random variable for VonMises.

See VonMises for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct von Mises distributions with given location and concentration.

The parameters loc and concentration must be shaped in a way that supports broadcasting (e.g. loc + concentration is a valid operation).

Parameters

loc – Floating point tensor, the circular means of the distribution(s).
concentration – Floating point tensor, the level of concentration of the distribution(s) around loc. Must take non-negative values. concentration = 0 defines a Uniform distribution, while concentration = +inf indicates a Deterministic distribution at loc.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

TypeError – if loc and concentration are different dtypes.

inferpy.models.VonMisesFisher(*args, **kwargs)¶

Create a random variable for VonMisesFisher.

See VonMisesFisher for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Creates a new VonMisesFisher instance.

Parameters

mean_direction – Floating-point Tensor with shape [B1, … Bn, D]. A unit vector indicating the mode of the distribution, or the unit-normalized direction of the mean. (This is not in general the mean of the distribution; the mean is not generally in the support of the distribution.) NOTE: D is currently restricted to <= 5.
concentration – Floating-point Tensor having batch shape [B1, … Bn] broadcastable with mean_direction. The level of concentration of samples around the mean_direction. concentration=0 indicates a uniform distribution over the unit hypersphere, and concentration=+inf indicates a Deterministic distribution (delta function) at mean_direction.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – For known-bad arguments, i.e. unsupported event dimension.

inferpy.models.Wishart(*args, **kwargs)¶

Create a random variable for Wishart.

See Wishart for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Construct Wishart distributions.

Parameters

df – float or double Tensor. Degrees of freedom, must be greater than or equal to dimension of the scale matrix.
scale – float or double Tensor. The symmetric positive definite scale matrix of the distribution. Exactly one of scale and ‘scale_tril` must be passed.
scale_tril – float or double Tensor. The Cholesky factorization of the symmetric positive definite scale matrix of the distribution. Exactly one of scale and ‘scale_tril` must be passed.
input_output_cholesky – Python bool. If True, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is True, input to log_prob is presumed of Cholesky form and output from sample, mean, and mode are of Cholesky form. Setting this argument to True is purely a computational optimization and does not change the underlying distribution; for instance, mean returns the Cholesky of the mean, not the mean of Cholesky factors. The variance and stddev methods are unaffected by this flag. Default value: False (i.e., input/output does not have Cholesky semantics).
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.
name – Python str name prefixed to Ops created by this class.

Raises

ValueError – if zero or both of ‘scale’ and ‘scale_tril’ are passed in.

inferpy.models.Zipf(*args, **kwargs)¶

Create a random variable for Zipf.

See Zipf for more details.

Returns: RandomVariable.

#### Original Docstring for Distribution

Initialize a batch of Zipf distributions.

Parameters

power – Float like Tensor representing the power parameter. Must be strictly greater than 1.
dtype – The dtype of Tensor returned by sample. Default value: tf.int32.
interpolate_nondiscrete – Python bool. When False, log_prob returns -inf (and prob returns 0) for non-integer inputs. When True, log_prob evaluates the continuous function -power log(k) - log(zeta(power)) , which matches the Zipf pmf at integer arguments k (note that this function is not itself a normalized probability log-density). Default value: True.
sample_maximum_iterations – Maximum number of iterations of allowable iterations in sample. When validate_args=True, samples which fail to reach convergence (subject to this cap) are masked out with self.dtype.min or nan depending on self.dtype.is_integer. Default value: 100.
validate_args – Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. Default value: False.
allow_nan_stats – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value “NaN” to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined. Default value: False.
name – Python str name prefixed to Ops created by this class. Default value: ‘Zipf’.

Raises

TypeError – if power is not float like.

inferpy.queries package¶

Submodules¶

inferpy.queries.query module¶

class inferpy.queries.query.Query(variables, target_names=None, data={})[source]¶

Bases: object

log_prob()[source]¶: Computes the log probabilities of a (set of) sample(s)

parameters(names=None)[source]¶

Return the parameters of the Random Variables of the model. If names is None, then return all the parameters of all the Random Variables. If names is a list, then return the parameters specified in the list (if exists) for all the Random Variables. If names is a dict, then return all the parameters specified (value) for each Random Variable (key).

NOTE: If tf_run=True, but any of the returned parameters is not a Tensor *and therefore cannot be evaluated): this returns a not evaluated dict (because the evaluation will raise an Exception)

Parameters: names – A list, a dict or None. Specify the parameters for the Random Variables to be obtained.
Returns: A dict, where the keys are the names of the Random Variables and the values a dict of parameters (name-value)

sample(size=1)[source]¶: Generates a sample for eache variable in the model

sum_log_prob()[source]¶: Computes the sum of the log probabilities (evaluated) of a (set of) sample(s)

inferpy.queries.query.flatten_result(f)[source]¶

Module contents¶

class inferpy.queries.Query(variables, target_names=None, data={})[source]¶

Bases: object

log_prob()[source]¶: Computes the log probabilities of a (set of) sample(s)

parameters(names=None)[source]¶

Return the parameters of the Random Variables of the model. If names is None, then return all the parameters of all the Random Variables. If names is a list, then return the parameters specified in the list (if exists) for all the Random Variables. If names is a dict, then return all the parameters specified (value) for each Random Variable (key).

NOTE: If tf_run=True, but any of the returned parameters is not a Tensor *and therefore cannot be evaluated): this returns a not evaluated dict (because the evaluation will raise an Exception)

Parameters: names – A list, a dict or None. Specify the parameters for the Random Variables to be obtained.
Returns: A dict, where the keys are the names of the Random Variables and the values a dict of parameters (name-value)

sample(size=1)[source]¶: Generates a sample for eache variable in the model

sum_log_prob()[source]¶: Computes the sum of the log probabilities (evaluated) of a (set of) sample(s)

inferpy.util package¶

Submodules¶

inferpy.util.interceptor module¶

inferpy.util.interceptor.set_values(**model_kwargs)[source]¶

Creates a value-setting interceptor. Usable as a parameter of the ed2.interceptor.

Model_kwargs: The name of each argument must be the name of a random variable to intercept, and the value is the element which intercepts the value of the random variable.
Returns: The random variable with the intercepted value

inferpy.util.interceptor.set_values_condition(var_condition, var_value)[source]¶

Creates a value-setting interceptor. Usable as a parameter of the ed2.interceptor.

Var_condition (tf.Variable)tf.Variable): The boolean tf.Variable, used to intercept the value property with value_var or the variable value property itself
Var_value (tf.Variable)tf.Variable): The tf.Variable used to intercept the value property when var_condition is True
Returns: The random variable with the intercepted value

inferpy.util.iterables module¶

inferpy.util.iterables.get_plate_size(variables, sample_dict)[source]¶

inferpy.util.iterables.get_shape(x)[source]¶

Get the shape of an element x. If it is an element with a shape attribute, return it. If it is a list with more than one element, compute the shape by checking the len, and the shape of internal elements. In that case, the shape must be consistent. Finally, in other case return () as shape.

Parameters: x – The element to compute its shape

:raises : class ValueError: list shape not consistent :returns: A tuple with the shape of x

inferpy.util.name module¶

inferpy.util.name.generate(prefix)[source]¶

This function is used to generate names based on an incremental counter (global variable in this module) dependent on the prefix (staring from 0 index)

Prefix (str)str): The begining of the random generated name
Returns: The generated random name

inferpy.util.runtime module¶

Module focused on evaluating tensors to makes the usage easier, forgetting about tensors and sessions

inferpy.util.runtime.runner_scope()[source]¶

inferpy.util.runtime.set_tf_run(enable)[source]¶

inferpy.util.runtime.tf_run_allowed(f)[source]¶: A function might return a tensor or not. In order to decide if the result of this function needs to be evaluated in a tf session or not, use the tf_run extra parameter or the tf_run_default value. If True, and this function is in the first level of execution depth, use a tf Session to evaluate the tensor or other evaluable object (like dicts)

inferpy.util.runtime.tf_run_ignored(f)[source]¶: A function might call other functions decorated with tf_run_allowed. This decorator is used to avoid that such functions are evaluated.

inferpy.util.runtime.try_run(obj)[source]¶

inferpy.util.session module¶

inferpy.util.session.clear_session()[source]¶

inferpy.util.session.get_session()[source]¶

inferpy.util.session.new_session(gpu_memory_fraction=0.0)[source]¶

inferpy.util.session.set_session(session)[source]¶

inferpy.util.session.swap_session(new_session)[source]¶

inferpy.util.tf_graph module¶

inferpy.util.tf_graph.get_empty_graph()[source]¶

inferpy.util.tf_graph.get_graph(varnames)[source]¶

Module contents¶

Package with modules defining functions, classes and variables which are useful for the main functionality provided by inferpy

inferpy.util.floatx()[source]¶

Returns the default float type, as a string. (e.g. ‘float16’, ‘float32’, ‘float64’). # Returns

# Example ```python

>>> inf.floatx()
'float32'

```

inferpy.util.set_floatx(floatx)[source]¶

Sets the default float type. # Arguments

# Example ```python

>>> from keras import backend as K
>>> inf.floatx()
'float32'
>>> inf.set_floatx('float16')
>>> inf..floatx()
'float16'

```

inferpy.util.set_tf_run(enable)[source]¶

inferpy.util.tf_run_allowed(f)[source]¶: A function might return a tensor or not. In order to decide if the result of this function needs to be evaluated in a tf session or not, use the tf_run extra parameter or the tf_run_default value. If True, and this function is in the first level of execution depth, use a tf Session to evaluate the tensor or other evaluable object (like dicts)

inferpy.util.tf_run_ignored(f)[source]¶: A function might call other functions decorated with tf_run_allowed. This decorator is used to avoid that such functions are evaluated.

inferpy.util.get_session()[source]¶

inferpy.util.set_session(session)[source]¶

inferpy.util.clear_session()[source]¶

Module contents¶

Contact and Support¶

If you have any question about the toolbox or if you want to collaborate in the project, please do not hesitate to contact us. You can do it through the following email address: inferpy.api@gmail.com

For more technical questions, please use Github issues.