tfp.distributions.Beta

Beta distribution.

Inherits From: AutoCompositeTensorDistribution, Distribution, AutoCompositeTensor

tfp.distributions.Beta(
    concentration1,
    concentration0,
    validate_args=False,
    allow_nan_stats=True,
    force_probs_to_zero_outside_support=False,
    name=&#x27;Beta'
)

The Beta distribution is defined over the (0, 1) interval using parameters concentration1 (aka 'alpha') and concentration0 (aka 'beta').

Mathematical Details

The probability density function (pdf) is,

pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z
Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta)

where:

concentration1 = alpha,
concentration0 = beta,
Z is the normalization constant, and,
Gamma is the gamma function.

The concentration parameters represent mean total counts of a 1 or a 0, i.e.,

concentration1 = alpha = mean * total_concentration
concentration0 = beta  = (1. - mean) * total_concentration

where mean in (0, 1) and total_concentration is a positive real number representing a mean total_count = concentration1 + concentration0.

Distribution parameters are automatically broadcast in all functions; see examples for details.

Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in the paper

Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients, 2018

Examples

import tensorflow_probability as tfp
tfd = tfp.distributions

# Create a batch of three Beta distributions.
alpha = [1, 2, 3]
beta = [1, 2, 3]
dist = tfd.Beta(alpha, beta)

dist.sample([4, 5])  # Shape [4, 5, 3]

# `x` has three batch entries, each with two samples.
x = [[.1, .4, .5],
     [.2, .3, .5]]
# Calculate the probability of each pair of samples under the corresponding
# distribution in `dist`.
dist.prob(x)         # Shape [2, 3]

# Define an equivalent Beta distribution parameterized by `mean` and
# `total_concentration`:
dist = tfd.Beta.experimental_from_mean_concentration(
  mean=0.5, total_concentration=alpha+beta)

# Create batch_shape=[2, 3] via parameter broadcast:
alpha = [[1.], [2]]      # Shape [2, 1]
beta = [3., 4, 5]        # Shape [3]
dist = tfd.Beta(alpha, beta)

# alpha broadcast as: [[1., 1, 1,],
#                      [2, 2, 2]]
# beta broadcast as:  [[3., 4, 5],
#                      [3, 4, 5]]
# batch_Shape [2, 3]
dist.sample([4, 5])  # Shape [4, 5, 2, 3]

x = [.2, .3, .5]
# x will be broadcast as [[.2, .3, .5],
#                         [.2, .3, .5]],
# thus matching batch_shape [2, 3].
dist.prob(x)         # Shape [2, 3]

Compute the gradients of samples w.r.t. the parameters:

alpha = tf.constant(1.0)
beta = tf.constant(2.0)
dist = tfd.Beta(alpha, beta)
samples = dist.sample(5)  # Shape [5]
loss = tf.reduce_mean(tf.square(samples))  # Arbitrary loss function
# Unbiased stochastic gradients of the loss function
grads = tf.gradients(loss, [alpha, beta])

Args
`concentration1`	Positive floating-point `Tensor` indicating mean number of successes; aka 'alpha'.
`concentration0`	Positive floating-point `Tensor` indicating mean number of failures; aka 'beta'.
`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.
`force_probs_to_zero_outside_support`	If `True`, force `prob(x) == 0` and `log_prob(x) == -inf` for values of x outside the distribution support.
`name`	Python `str` name prefixed to Ops created by this class.

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.
`concentration0`	Concentration parameter associated with a `0` outcome.
`concentration1`	Concentration parameter associated with a `1` outcome.
`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.
`experimental_shard_axis_names`	The list or structure of lists of active shard axis names.
`force_probs_to_zero_outside_support`
`name`	Name prepended to all ops created by this `Distribution`.
`name_scope`	Returns a `tf.name_scope` instance for this class.
`non_trainable_variables`	Sequence of non-trainable variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.
`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 `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`.
`submodules`	Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). `a = tf.Module()` `b = tf.Module()` `c = tf.Module()` `a.b = b` `b.c = c` `list(a.submodules) == [b, c]` `True` `list(b.submodules) == [c]` `True` `list(c.submodules) == []` `True`
`trainable_variables`	Sequence of trainable variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.
`validate_args`	Python `bool` indicating possibly expensive checks are enabled.
`variables`	Sequence of variables owned by this module and its submodules. Note: this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change.

Methods

`batch_shape_tensor`

View source

batch_shape_tensor(
    name=&#x27;batch_shape_tensor'
)

Shape of a single sample from a single event index as a 1-D Tensor.

The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

Args
`name`	name to give to the op

Returns
`batch_shape`	`Tensor`.

`cdf`

View source

cdf(
    value, name=&#x27;cdf', **kwargs
)

Cumulative distribution function.

Given random variable X, the cumulative distribution function cdf is:

cdf(x) := P[X <= x]

Additional documentation from Beta:

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`cdf`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`copy`

View source

copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

Args
`**override_parameters_kwargs`	String/value dictionary of initialization arguments to override with new values.

Returns
`distribution`	A new instance of `type(self)` initialized from the union of self.parameters and override_parameters_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`.

`covariance`

View source

covariance(
    name=&#x27;covariance', **kwargs
)

Covariance.

Covariance is (possibly) defined only for non-scalar-event distributions.

For example, for a length-k, vector-valued distribution, it is calculated as,

Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]

where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation.

Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e.,

Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]

where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

Args
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`covariance`	Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`.

`cross_entropy`

View source

cross_entropy(
    other, name=&#x27;cross_entropy'
)

Computes the (Shannon) cross entropy.

Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shannon) cross entropy is defined as:

H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)

where F denotes the support of the random variable X ~ P.

other types with built-in registrations: Beta

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

Returns
`cross_entropy`	`self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy.

`entropy`

View source

entropy(
    name=&#x27;entropy', **kwargs
)

Shannon entropy in nats.

`event_shape_tensor`

View source

event_shape_tensor(
    name=&#x27;event_shape_tensor'
)

Shape of a single sample from a single batch as a 1-D int32 Tensor.

Args
`name`	name to give to the op

Returns
`event_shape`	`Tensor`.

`experimental_default_event_space_bijector`

View source

experimental_default_event_space_bijector(
    *args, **kwargs
)

Bijector mapping the reals (R**n) to the event space of the distribution.

Distributions with continuous support may implement _default_event_space_bijector which returns a subclass of tfp.bijectors.Bijector that maps R**n to the distribution's event space. For example, the default bijector for the Beta distribution is tfp.bijectors.Sigmoid(), which maps the real line to [0, 1], the support of the Beta distribution. The default bijector for the CholeskyLKJ distribution is tfp.bijectors.CorrelationCholesky, which maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal.

The purpose of experimental_default_event_space_bijector is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential.

For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns None.

Args
`*args`	Passed to implementation `_default_event_space_bijector`.
`**kwargs`	Passed to implementation `_default_event_space_bijector`.

Returns
`event_space_bijector`	`Bijector` instance or `None`.

`experimental_fit`

View source

@classmethod
experimental_fit(
    value, sample_ndims=1, validate_args=False, **init_kwargs
)

Instantiates a distribution that maximizes the likelihood of x.

Args
`value`	a `Tensor` valid sample from this distribution family.
`sample_ndims`	Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. 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`.
`**init_kwargs`	Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`.

Returns
`maximum_likelihood_instance`	instance of `cls` with parameters that maximize the likelihood of `value`.

`experimental_from_mean_concentration`

View source

@classmethod
experimental_from_mean_concentration(
    mean, total_concentration, **kwargs
)

Constructs a Beta from its mean and total concentration.

Experimental: Naming, location of this API may change.

Total concentration, sometimes called "sample size", is the sum of the two concentration parameters (concentration1 and concentration0 in __init__).

Args
`mean`	The mean of the constructed distribution.
`total_concentration`	The sum of the two concentration parameters. Must be greater than 0.
`**kwargs`	Other keyword arguments passed directly to `__init__`, e.g. `validate_args`.

Returns
`beta`	A distribution with the given parameterization.

`experimental_from_mean_variance`

View source

@classmethod
experimental_from_mean_variance(
    mean, variance, **kwargs
)

Constructs a Beta from its mean and variance.

Experimental: Naming, location of this API may change.

Variance must be less than mean * (1. - mean), and in particular less than the maximal variance of 0.25, which occurs with mean = 0.5.

Args
`mean`	The mean of the constructed distribution.
`variance`	The variance of the constructed distribution.
`**kwargs`	Other keyword arguments passed directly to `__init__`, e.g. `validate_args`.

Returns
`beta`	A distribution with the given parameterization.

`experimental_local_measure`

View source

experimental_local_measure(
    value, backward_compat=False, **kwargs
)

Returns a log probability density together with a TangentSpace.

A TangentSpace allows us to calculate the correct push-forward density when we apply a transformation to a Distribution on a strict submanifold of R^n (typically via a Bijector in the TransformedDistribution subclass). The density correction uses the basis of the tangent space.

Args
`value`	`float` or `double` `Tensor`.
`backward_compat`	`bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R^n with the standard basis.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`log_prob`	a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.
`tangent_space`	a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`.

Raises
UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined.

`experimental_sample_and_log_prob`

View source

experimental_sample_and_log_prob(
    sample_shape=(), seed=None, name=&#x27;sample_and_log_prob', **kwargs
)

Samples from this distribution and returns the log density of the sample.

The default implementation simply calls sample and log_prob:

def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
  x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
  return x, self.log_prob(x, **kwargs)

However, some subclasses may provide more efficient and/or numerically stable implementations.

Args
`sample_shape`	integer `Tensor` desired shape of samples to draw. Default value: `()`.
`seed`	PRNG seed; see `tfp.random.sanitize_seed` for details. Default value: `None`.
`name`	name to give to the op. Default value: `'sample_and_log_prob'`.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`samples`	a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`.
`log_prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`is_scalar_batch`

View source

is_scalar_batch(
    name=&#x27;is_scalar_batch'
)

Indicates that batch_shape == [].

Args
`name`	Python `str` prepended to names of ops created by this function.

Returns
`is_scalar_batch`	`bool` scalar `Tensor`.

`is_scalar_event`

View source

is_scalar_event(
    name=&#x27;is_scalar_event'
)

Indicates that event_shape == [].

Args
`name`	Python `str` prepended to names of ops created by this function.

Returns
`is_scalar_event`	`bool` scalar `Tensor`.

`kl_divergence`

View source

kl_divergence(
    other, name=&#x27;kl_divergence'
)

Computes the Kullback--Leibler divergence.

Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as:

KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]

where F denotes the support of the random variable X ~ p, H[., .] denotes (Shannon) cross entropy, and H[.] denotes (Shannon) entropy.

other types with built-in registrations: Beta

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

Returns
`kl_divergence`	`self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of the Kullback-Leibler divergence.

`log_cdf`

View source

log_cdf(
    value, name=&#x27;log_cdf', **kwargs
)

Log cumulative distribution function.

Given random variable X, the cumulative distribution function cdf is:

log_cdf(x) := Log[ P[X <= x] ]

Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

Additional documentation from Beta:

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`logcdf`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`log_prob`

View source

log_prob(
    value, name=&#x27;log_prob', **kwargs
)

Log probability density/mass function.

Additional documentation from Beta:

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`log_prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`log_survival_function`

View source

log_survival_function(
    value, name=&#x27;log_survival_function', **kwargs
)

Log survival function.

Given random variable X, the survival function is defined:

log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]

Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`mean`

View source

mean(
    name=&#x27;mean', **kwargs
)

Mean.

`mode`

View source

mode(
    name=&#x27;mode', **kwargs
)

Mode.

Additional documentation from Beta:

`param_shapes`

View source

@classmethod
param_shapes(
    sample_shape, name=&#x27;DistributionParamShapes'
)

Shapes of parameters given the desired shape of a call to sample(). (deprecated)

This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample().

Subclasses should override class method _param_shapes.

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

Returns
`dict` of parameter name to `Tensor` shapes.

`param_static_shapes`

View source

@classmethod
param_static_shapes(
    sample_shape
)

param_shapes with static (i.e. TensorShape) shapes. (deprecated)

This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically.

Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

Args
`sample_shape`	`TensorShape` or python list/tuple. Desired shape of a call to `sample()`.

Returns
`dict` of parameter name to `TensorShape`.

Raises
`ValueError`	if `sample_shape` is a `TensorShape` and is not fully defined.

`parameter_properties`

View source

@classmethod
parameter_properties(
    dtype=tf.float32, num_classes=None
)

Returns a dict mapping constructor arg names to property annotations.

This dict should include an entry for each of the distribution's Tensor-valued constructor arguments.

Distribution subclasses are not required to implement _parameter_properties, so this method may raise NotImplementedError. Providing a _parameter_properties implementation enables several advanced features, including:

Distribution batch slicing (sliced_distribution = distribution[i:j]).
Automatic inference of _batch_shape and _batch_shape_tensor, which must otherwise be computed explicitly.
Automatic instantiation of the distribution within TFP's internal property tests.
Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.

In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from tf.vectorized_map.

Args
`dtype`	Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed.
`num_classes`	Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored.

Returns
`parameter_properties`	A `str ->`tfp.python.internal.parameter_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties` instances.

Raises
`NotImplementedError`	if the distribution class does not implement `_parameter_properties`.

`prob`

View source

prob(
    value, name=&#x27;prob', **kwargs
)

Probability density/mass function.

Additional documentation from Beta:

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`quantile`

View source

quantile(
    value, name=&#x27;quantile', **kwargs
)

Quantile function. Aka 'inverse cdf' or 'percent point function'.

Given random variable X and p in [0, 1], the quantile is:

quantile(p) := x such that P[X <= x] == p

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`quantile`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`sample`

View source

sample(
    sample_shape=(), seed=None, name=&#x27;sample', **kwargs
)

Generate samples of the specified shape.

Note that a call to sample() without arguments will generate a single sample.

Args
`sample_shape`	0D or 1D `int32` `Tensor`. Shape of the generated samples.
`seed`	PRNG seed; see `tfp.random.sanitize_seed` for details.
`name`	name to give to the op.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`samples`	a `Tensor` with prepended dimensions `sample_shape`.

`stddev`

View source

stddev(
    name=&#x27;stddev', **kwargs
)

Standard deviation.

Standard deviation is defined as,

stddev = E[(X - E[X])**2]**0.5

where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

Args
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`stddev`	Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`.

`survival_function`

View source

survival_function(
    value, name=&#x27;survival_function', **kwargs
)

Survival function.

Given random variable X, the survival function is defined:

survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`unnormalized_log_prob`

View source

unnormalized_log_prob(
    value, name=&#x27;unnormalized_log_prob', **kwargs
)

Potentially unnormalized log probability density/mass function.

This function is similar to log_prob, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls log_prob.

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`unnormalized_log_prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`variance`

View source

variance(
    name=&#x27;variance', **kwargs
)

Variance.

Variance is defined as,

Var = E[(X - E[X])**2]

where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

Args
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`variance`	Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`.

`with_name_scope`

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

class MyModule(tf.Module):
  @tf.Module.with_name_scope
  def __call__(self, x):
    if not hasattr(self, &#x27;w'):
      self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
    return tf.matmul(x, self.w)

Using the above module would produce tf.Variables and tf.Tensors whose names included the module name:

mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable &#x27;my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>

Args
`method`	The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

`getitem`

View source

__getitem__(
    slices
)

Slices the batch axes of this distribution, returning a new instance.

b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape  # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape  # => [3, 1, 5, 2, 4]

x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.batch_shape  # => [4, 5, 3]
mvn.event_shape  # => [2]
mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
mvn2.batch_shape  # => [4, 2, 3, 1]
mvn2.event_shape  # => [2]

Args
`slices`	slices from the [] operator

Returns
`dist`	A new `tfd.Distribution` instance with sliced parameters.

`iter`

View source

__iter__()

tfp.distributions.Beta

Mathematical Details

Examples

Args

Attributes

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

experimental_default_event_space_bijector

experimental_fit

experimental_from_mean_concentration

experimental_from_mean_variance

experimental_local_measure

experimental_sample_and_log_prob

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

parameter_properties

prob

quantile

sample

stddev

survival_function

unnormalized_log_prob

variance

with_name_scope

__getitem__

__iter__

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`experimental_default_event_space_bijector`

`experimental_fit`

`experimental_from_mean_concentration`

`experimental_from_mean_variance`

`experimental_local_measure`

`experimental_sample_and_log_prob`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`parameter_properties`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`unnormalized_log_prob`

`variance`

`with_name_scope`

`getitem`

`iter`