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tf.compat.v1.distributions.Distribution

A generic probability distribution base class.

tf.compat.v1.distributions.Distribution(
    dtype, reparameterization_type, validate_args, allow_nan_stats, parameters=None,
    graph_parents=None, name=None
)

Distribution is a base class for constructing and organizing properties (e.g., mean, variance) of random variables (e.g, Bernoulli, Gaussian).

Subclassing

Subclasses are expected to implement a leading-underscore version of the same-named function. The argument signature should be identical except for the omission of name="...". For example, to enable log_prob(value, name="log_prob") a subclass should implement _log_prob(value).

Subclasses can append to public-level docstrings by providing docstrings for their method specializations. For example:

@util.AppendDocstring("Some other details.")
def _log_prob(self, value):
  ...

would add the string "Some other details." to the log_prob function docstring. This is implemented as a simple decorator to avoid python linter complaining about missing Args/Returns/Raises sections in the partial docstrings.

Broadcasting, batching, and shapes

All distributions support batches of independent distributions of that type. The batch shape is determined by broadcasting together the parameters.

The shape of arguments to __init__, cdf, log_cdf, prob, and log_prob reflect this broadcasting, as does the return value of sample and sample_n.

sample_n_shape = [n] + batch_shape + event_shape, where sample_n_shape is the shape of the Tensor returned from sample_n, n is the number of samples, batch_shape defines how many independent distributions there are, and event_shape defines the shape of samples from each of those independent distributions. Samples are independent along the batch_shape dimensions, but not necessarily so along the event_shape dimensions (depending on the particulars of the underlying distribution).

Using the Uniform distribution as an example:

minval = 3.0
maxval = [[4.0, 6.0],
          [10.0, 12.0]]

# Broadcasting:
# This instance represents 4 Uniform distributions. Each has a lower bound at
# 3.0 as the `minval` parameter was broadcasted to match `maxval`'s shape.
u = Uniform(minval, maxval)

# `event_shape` is `TensorShape([])`.
event_shape = u.event_shape
# `event_shape_t` is a `Tensor` which will evaluate to [].
event_shape_t = u.event_shape_tensor()

# Sampling returns a sample per distribution. `samples` has shape
# [5, 2, 2], which is [n] + batch_shape + event_shape, where n=5,
# batch_shape=[2, 2], and event_shape=[].
samples = u.sample_n(5)

# The broadcasting holds across methods. Here we use `cdf` as an example. The
# same holds for `log_cdf` and the likelihood functions.

# `cum_prob` has shape [2, 2] as the `value` argument was broadcasted to the
# shape of the `Uniform` instance.
cum_prob_broadcast = u.cdf(4.0)

# `cum_prob`'s shape is [2, 2], one per distribution. No broadcasting
# occurred.
cum_prob_per_dist = u.cdf([[4.0, 5.0],
                           [6.0, 7.0]])

# INVALID as the `value` argument is not broadcastable to the distribution's
# shape.
cum_prob_invalid = u.cdf([4.0, 5.0, 6.0])

Shapes

There are three important concepts associated with TensorFlow Distributions shapes:

Event shape describes the shape of a single draw from the distribution; it may be dependent across dimensions. For scalar distributions, the event shape is []. For a 5-dimensional MultivariateNormal, the event shape is [5].
Batch shape describes independent, not identically distributed draws, aka a "collection" or "bunch" of distributions.
Sample shape describes independent, identically distributed draws of batches from the distribution family.

The event shape and the batch shape are properties of a Distribution object, whereas the sample shape is associated with a specific call to sample or log_prob.

For detailed usage examples of TensorFlow Distributions shapes, see this tutorial

Parameter values leading to undefined statistics or distributions.

Some distributions do not have well-defined statistics for all initialization parameter values. For example, the beta distribution is parameterized by positive real numbers concentration1 and concentration0, and does not have well-defined mode if concentration1 < 1 or concentration0 < 1.

The user is given the option of raising an exception or returning NaN.

a = tf.exp(tf.matmul(logits, weights_a))
b = tf.exp(tf.matmul(logits, weights_b))

# Will raise exception if ANY batch member has a < 1 or b < 1.
dist = distributions.beta(a, b, allow_nan_stats=False)
mode = dist.mode().eval()

# Will return NaN for batch members with either a < 1 or b < 1.
dist = distributions.beta(a, b, allow_nan_stats=True)  # Default behavior
mode = dist.mode().eval()

In all cases, an exception is raised if invalid parameters are passed, e.g.

# Will raise an exception if any Op is run.
negative_a = -1.0 * a  # beta distribution by definition has a > 0.
dist = distributions.beta(negative_a, b, allow_nan_stats=True)
dist.mean().eval()

Args
`dtype`	The type of the event samples. `None` implies no type-enforcement.
`reparameterization_type`	Instance of `ReparameterizationType`. If `distributions.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 `distributions.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`.

Attributes
`allow_nan_stats`	Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.
`batch_shape`	Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
`dtype`	The `DType` of `Tensor`s handled by this `Distribution`.
`event_shape`	Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown.
`name`	Name prepended to all ops created by this `Distribution`.
`parameters`	Dictionary of parameters used to instantiate this `Distribution`.
`reparameterization_type`	Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `distributions.FULLY_REPARAMETERIZED` or `distributions.NOT_REPARAMETERIZED`.
`validate_args`	Python `bool` indicating possibly expensive checks are enabled.

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.

Args
`other`	`tfp.distributions.Distribution` instance.
`name`	Python `str` prepended to names of ops created by this function.

Args
`sample_shape`	`Tensor` or python list/tuple. Desired shape of a call to `sample()`.
`name`	name to prepend ops with.

Args
`sample_shape`	0D or 1D `int32` `Tensor`. Shape of the generated samples.
`seed`	Python integer seed for RNG
`name`	name to give to the op.

tf.compat.v1.distributions.Distribution

Subclassing

Broadcasting, batching, and shapes

Shapes

Parameter values leading to undefined statistics or distributions.

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

prob

quantile

sample

stddev

survival_function

variance

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`variance`