tf.contrib.distributions.ConditionalDistribution

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Class ConditionalDistribution

Distribution that supports intrinsic parameters (local latents).

Inherits From: Distribution

Subclasses of this distribution may have additional keyword arguments passed to their sample-based methods (i.e. sample, log_prob, etc.).

__init__

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__init__(
    dtype,
    reparameterization_type,
    validate_args,
    allow_nan_stats,
    parameters=None,
    graph_parents=None,
    name=None
)

Constructs the Distribution. (deprecated)

This is a private method for subclass use.

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.

Properties

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.

Returns:

  • allow_nan_stats: Python bool.

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.

Returns:

  • batch_shape: TensorShape, possibly unknown.

dtype

The DType of Tensors handled by this Distribution.

event_shape

Shape of a single sample from a single batch as a TensorShape.

May be partially defined or unknown.

Returns:

  • event_shape: TensorShape, possibly 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.

Returns:

An instance of ReparameterizationType.

validate_args

Python bool indicating possibly expensive checks are enabled.

Methods

tf.contrib.distributions.ConditionalDistribution.batch_shape_tensor

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batch_shape_tensor(name='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.

tf.contrib.distributions.ConditionalDistribution.cdf

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cdf(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.copy

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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).

tf.contrib.distributions.ConditionalDistribution.covariance

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covariance(name='covariance')

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.

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).

tf.contrib.distributions.ConditionalDistribution.cross_entropy

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cross_entropy(
    other,
    name='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), (Shanon) 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.

Args:

Returns:

  • cross_entropy: self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.

tf.contrib.distributions.ConditionalDistribution.entropy

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entropy(name='entropy')

Shannon entropy in nats.

tf.contrib.distributions.ConditionalDistribution.event_shape_tensor

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event_shape_tensor(name='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.

tf.contrib.distributions.ConditionalDistribution.is_scalar_batch

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is_scalar_batch(name='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.

tf.contrib.distributions.ConditionalDistribution.is_scalar_event

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is_scalar_event(name='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.

tf.contrib.distributions.ConditionalDistribution.kl_divergence

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kl_divergence(
    other,
    name='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 (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

Args:

Returns:

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

tf.contrib.distributions.ConditionalDistribution.log_cdf

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log_cdf(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.log_prob

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log_prob(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.log_survival_function

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log_survival_function(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.mean

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mean(name='mean')

Mean.

tf.contrib.distributions.ConditionalDistribution.mode

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mode(name='mode')

Mode.

tf.contrib.distributions.ConditionalDistribution.param_shapes

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param_shapes(
    cls,
    sample_shape,
    name='DistributionParamShapes'
)

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

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.

tf.contrib.distributions.ConditionalDistribution.param_static_shapes

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param_static_shapes(
    cls,
    sample_shape
)

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

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.

tf.contrib.distributions.ConditionalDistribution.prob

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prob(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.quantile

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quantile(
    value,
    name='quantile'
)

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.

Returns:

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

tf.contrib.distributions.ConditionalDistribution.sample

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sample(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.stddev

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stddev(name='stddev')

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.

Returns:

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

tf.contrib.distributions.ConditionalDistribution.survival_function

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survival_function(
    *args,
    **kwargs
)
kwargs:
  • **condition_kwargs: Named arguments forwarded to subclass implementation.

tf.contrib.distributions.ConditionalDistribution.variance

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variance(name='variance')

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.

Returns:

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