Statistical distributions (contrib)

[TOC]

Classes representing statistical distributions and ops for working with them.

Classes for statistical distributions.

Classes that represent batches of statistical distributions. Each class is initialized with parameters that define the distributions.

Base classes

class tf.contrib.distributions.Distribution

A generic probability distribution base class.

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

Subclassing

Subclasess 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:

@distribution_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.get_event_shape()
# `event_shape_t` is a `Tensor` which will evaluate to [].
event_shape_t = u.event_shape

# 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])

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 a and b, and does not have well-defined mode if a < 1 or b < 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()

tf.contrib.distributions.Distribution.__init__(dtype, parameters, is_continuous, is_reparameterized, validate_args, allow_nan_stats, name=None)

Constructs the Distribution.

This is a private method for subclass use.

Args:

• dtype: The type of the event samples. None implies no type-enforcement.
• parameters: Python dictionary of parameters used by this Distribution.
• is_continuous: Python boolean. If True this Distribution is continuous over its supported domain.
• is_reparameterized: Python boolean. If True 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.
• validate_args: Python boolean. 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 boolean. If False, raise an exception if a statistic (e.g., mean, mode) 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).

tf.contrib.distributions.Distribution.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Distribution.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Distribution.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Distribution.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Distribution.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.Distribution.event_shape(name='event_shape')

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.Distribution.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Distribution.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Distribution.is_continuous

tf.contrib.distributions.Distribution.is_reparameterized

tf.contrib.distributions.Distribution.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Distribution.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Distribution.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Distribution.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Distribution.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Distribution.mean(name='mean')

Mean.

tf.contrib.distributions.Distribution.mode(name='mode')

Mode.

tf.contrib.distributions.Distribution.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Distribution.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Distribution.param_static_shapes(cls, sample_shape)

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

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.Distribution.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Distribution.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Distribution.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Distribution.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Distribution.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Distribution.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Distribution.std(name='std')

Standard deviation.

tf.contrib.distributions.Distribution.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Distribution.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Distribution.variance(name='variance')

Variance.

Univariate (scalar) distributions

class tf.contrib.distributions.Binomial

Binomial distribution.

This distribution is parameterized by a vector p of probabilities and n, the total counts.

Mathematical details

The Binomial is a distribution over the number of successes in n independent trials, with each trial having the same probability of success p. The probability mass function (pmf):

pmf(k) = n! / (k! * (n - k)!) * (p)^k * (1 - p)^(n - k)

Examples

Create a single distribution, corresponding to 5 coin flips.

dist = Binomial(n=5., p=.5)

Create a single distribution (using logits), corresponding to 5 coin flips.

dist = Binomial(n=5., logits=0.)

Creates 3 distributions with the third distribution most likely to have successes.

p = [.2, .3, .8]
# n will be broadcast to [4., 4., 4.], to match p.
dist = Binomial(n=4., p=p)

The distribution functions can be evaluated on counts.

# counts same shape as p.
counts = [1., 2, 3]
dist.prob(counts)  # Shape [3]

# p will be broadcast to [[.2, .3, .8], [.2, .3, .8]] to match counts.
counts = [[1., 2, 1], [2, 2, 4]]
dist.prob(counts)  # Shape [2, 3]

# p will be broadcast to shape [5, 7, 3] to match counts.
counts = [[...]]  # Shape [5, 7, 3]
dist.prob(counts)  # Shape [5, 7, 3]

tf.contrib.distributions.Binomial.__init__(n, logits=None, p=None, validate_args=False, allow_nan_stats=True, name='Binomial')

Initialize a batch of Binomial distributions.

Args:

• n: Non-negative floating point tensor with shape broadcastable to [N1,..., Nm] with m >= 0 and the same dtype as p 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 n. Each entry represents logits for the probability of success for independent Binomial distributions.
• p: Positive floating point tensor with shape broadcastable to [N1,..., Nm] m >= 0, p in [0, 1]. Each entry represents the probability of success for independent Binomial distributions.
• validate_args: Boolean, default False. Whether to assert valid values for parameters n, p, and x in prob and log_prob. If False and inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prefix Ops created by this distribution class.

• Examples:

# Define 1-batch of a binomial distribution.
dist = Binomial(n=2., p=.9)

# Define a 2-batch.
dist = Binomial(n=[4., 5], p=[.1, .3])

tf.contrib.distributions.Binomial.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Binomial.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Binomial.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Binomial.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Binomial.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.Binomial.event_shape(name='event_shape')

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.Binomial.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Binomial.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Binomial.is_continuous

tf.contrib.distributions.Binomial.is_reparameterized

tf.contrib.distributions.Binomial.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Binomial.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Binomial.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Binomial.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Additional documentation from Binomial:

For each batch member of counts value, P[counts] is the probability that after sampling n draws from this Binomial distribution, the number of successes is k. Note that different sequences of draws can result in the same counts, thus the probability includes a combinatorial coefficient.

value must be a non-negative tensor with dtype dtype and whose shape can be broadcast with self.p and self.n. counts is only legal if it is less than or equal to n and its components are equal to integer values.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Binomial.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Binomial.logits

Log-odds.

tf.contrib.distributions.Binomial.mean(name='mean')

Mean.

tf.contrib.distributions.Binomial.mode(name='mode')

Mode.

Additional documentation from Binomial:

Note that when (n + 1) * p is an integer, there are actually two modes. Namely, (n + 1) * p and (n + 1) * p - 1 are both modes. Here we return only the larger of the two modes.

tf.contrib.distributions.Binomial.n

Number of trials.

tf.contrib.distributions.Binomial.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Binomial.p

Probability of success.

tf.contrib.distributions.Binomial.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Binomial.param_static_shapes(cls, sample_shape)

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

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.Binomial.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Binomial.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Binomial.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Binomial.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Additional documentation from Binomial:

For each batch member of counts value, P[counts] is the probability that after sampling n draws from this Binomial distribution, the number of successes is k. Note that different sequences of draws can result in the same counts, thus the probability includes a combinatorial coefficient.

value must be a non-negative tensor with dtype dtype and whose shape can be broadcast with self.p and self.n. counts is only legal if it is less than or equal to n and its components are equal to integer values.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Binomial.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Binomial.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Binomial.std(name='std')

Standard deviation.

tf.contrib.distributions.Binomial.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Binomial.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Binomial.variance(name='variance')

Variance.

class tf.contrib.distributions.Bernoulli

Bernoulli distribution.

The Bernoulli distribution is parameterized by p, the probability of a positive event.

tf.contrib.distributions.Bernoulli.__init__(logits=None, p=None, dtype=tf.int32, validate_args=False, allow_nan_stats=True, name='Bernoulli')

Construct Bernoulli distributions.

Args:

• logits: An N-D Tensor representing the log-odds of a positive event. Each entry in the Tensor parametrizes an independent Bernoulli distribution where the probability of an event is sigmoid(logits).
• p: An N-D Tensor representing the probability of a positive event. Each entry in the Tensor parameterizes an independent Bernoulli distribution.
• dtype: dtype for samples.
• validate_args: Boolean, default False. Whether to validate that 0 <= p <= 1. If validate_args is False, and the inputs are invalid, methods like log_pmf may return NaN values.
• 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.
• name: A name for this distribution.

Raises:

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

tf.contrib.distributions.Bernoulli.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Bernoulli.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Bernoulli.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Bernoulli.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Bernoulli.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.Bernoulli.event_shape(name='event_shape')

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.Bernoulli.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Bernoulli.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Bernoulli.is_continuous

tf.contrib.distributions.Bernoulli.is_reparameterized

tf.contrib.distributions.Bernoulli.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Bernoulli.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Bernoulli.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Bernoulli.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Bernoulli.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Bernoulli.logits

tf.contrib.distributions.Bernoulli.mean(name='mean')

Mean.

tf.contrib.distributions.Bernoulli.mode(name='mode')

Mode.

Additional documentation from Bernoulli:

Returns 1 if p > 1-p and 0 otherwise.

tf.contrib.distributions.Bernoulli.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Bernoulli.p

tf.contrib.distributions.Bernoulli.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Bernoulli.param_static_shapes(cls, sample_shape)

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

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.Bernoulli.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Bernoulli.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Bernoulli.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Bernoulli.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Bernoulli.q

1-p.

tf.contrib.distributions.Bernoulli.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Bernoulli.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Bernoulli.std(name='std')

Standard deviation.

tf.contrib.distributions.Bernoulli.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Bernoulli.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Bernoulli.variance(name='variance')

Variance.

class tf.contrib.distributions.BernoulliWithSigmoidP

Bernoulli with p = sigmoid(p).

tf.contrib.distributions.BernoulliWithSigmoidP.__init__(p=None, dtype=tf.int32, validate_args=False, allow_nan_stats=True, name='BernoulliWithSigmoidP')

tf.contrib.distributions.BernoulliWithSigmoidP.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.BernoulliWithSigmoidP.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.BernoulliWithSigmoidP.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BernoulliWithSigmoidP.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.BernoulliWithSigmoidP.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.BernoulliWithSigmoidP.event_shape(name='event_shape')

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.BernoulliWithSigmoidP.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.BernoulliWithSigmoidP.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.BernoulliWithSigmoidP.is_continuous

tf.contrib.distributions.BernoulliWithSigmoidP.is_reparameterized

tf.contrib.distributions.BernoulliWithSigmoidP.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BernoulliWithSigmoidP.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.BernoulliWithSigmoidP.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.BernoulliWithSigmoidP.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BernoulliWithSigmoidP.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.BernoulliWithSigmoidP.logits

tf.contrib.distributions.BernoulliWithSigmoidP.mean(name='mean')

Mean.

tf.contrib.distributions.BernoulliWithSigmoidP.mode(name='mode')

Mode.

Additional documentation from Bernoulli:

Returns 1 if p > 1-p and 0 otherwise.

tf.contrib.distributions.BernoulliWithSigmoidP.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.BernoulliWithSigmoidP.p

tf.contrib.distributions.BernoulliWithSigmoidP.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.BernoulliWithSigmoidP.param_static_shapes(cls, sample_shape)

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

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.BernoulliWithSigmoidP.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.BernoulliWithSigmoidP.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.BernoulliWithSigmoidP.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.BernoulliWithSigmoidP.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BernoulliWithSigmoidP.q

1-p.

tf.contrib.distributions.BernoulliWithSigmoidP.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.BernoulliWithSigmoidP.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.BernoulliWithSigmoidP.std(name='std')

Standard deviation.

tf.contrib.distributions.BernoulliWithSigmoidP.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.BernoulliWithSigmoidP.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.BernoulliWithSigmoidP.variance(name='variance')

Variance.

class tf.contrib.distributions.Beta

Beta distribution.

This distribution is parameterized by a and b which are shape parameters.

Mathematical details

The Beta is a distribution over the interval (0, 1). The distribution has hyperparameters a and b and probability mass function (pdf):

pdf(x) = 1 / Beta(a, b) * x^(a - 1) * (1 - x)^(b - 1)

where Beta(a, b) = Gamma(a) * Gamma(b) / Gamma(a + b) is the beta function.

This class provides methods to create indexed batches of Beta distributions. One entry of the broadcasted shape represents of a and b represents one single Beta distribution. When calling distribution functions (e.g. dist.pdf(x)), a, b and x are broadcast to the same shape (if possible). Every entry in a/b/x corresponds to a single Beta distribution.

Examples

Creates 3 distributions. The distribution functions can be evaluated on x.

a = [1, 2, 3]
b = [1, 2, 3]
dist = Beta(a, b)

# x same shape as a.
x = [.2, .3, .7]
dist.pdf(x)  # Shape [3]

# a/b will be broadcast to [[1, 2, 3], [1, 2, 3]] to match x.
x = [[.1, .4, .5], [.2, .3, .5]]
dist.pdf(x)  # Shape [2, 3]

# a/b will be broadcast to shape [5, 7, 3] to match x.
x = [[...]]  # Shape [5, 7, 3]
dist.pdf(x)  # Shape [5, 7, 3]

Creates a 2-batch of 3-class distributions.

a = [[1, 2, 3], [4, 5, 6]]  # Shape [2, 3]
b = 5  # Shape []
dist = Beta(a, b)

# x will be broadcast to [[.2, .3, .9], [.2, .3, .9]] to match a/b.
x = [.2, .3, .9]
dist.pdf(x)  # Shape [2]

tf.contrib.distributions.Beta.__init__(a, b, validate_args=False, allow_nan_stats=True, name='Beta')

Initialize a batch of Beta distributions.

Args:

• a: Positive floating point tensor with shape broadcastable to [N1,..., Nm] m >= 0. Defines this as a batch of N1 x ... x Nm different Beta distributions. This also defines the dtype of the distribution.
• b: Positive floating point tensor with shape broadcastable to [N1,..., Nm] m >= 0. Defines this as a batch of N1 x ... x Nm different Beta distributions.
• validate_args: Boolean, default False. Whether to assert valid values for parameters a, b, and x in prob and log_prob. If False and inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prefix Ops created by this distribution class.

• Examples:

# Define 1-batch.
dist = Beta(1.1, 2.0)

# Define a 2-batch.
dist = Beta([1.0, 2.0], [4.0, 5.0])

tf.contrib.distributions.Beta.a

Shape parameter.

tf.contrib.distributions.Beta.a_b_sum

Sum of parameters.

tf.contrib.distributions.Beta.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Beta.b

Shape parameter.

tf.contrib.distributions.Beta.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Beta.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Beta.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Beta.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.Beta.event_shape(name='event_shape')

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.Beta.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Beta.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Beta.is_continuous

tf.contrib.distributions.Beta.is_reparameterized

tf.contrib.distributions.Beta.log_cdf(value, name='log_cdf')

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:

Note that the argument x must be a non-negative floating point tensor whose shape can be broadcast with self.a and self.b. For fixed leading dimensions, the last dimension represents counts for the corresponding Beta distribution in self.a and self.b. x is only legal if 0 < x < 1.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Beta.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Beta.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Beta.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Beta.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Beta.mean(name='mean')

Mean.

tf.contrib.distributions.Beta.mode(name='mode')

Mode.

Additional documentation from Beta:

Note that the mode for the Beta distribution is only defined when a > 1, b > 1. This returns the mode when a > 1 and b > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.Beta.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Beta.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Beta.param_static_shapes(cls, sample_shape)

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

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.Beta.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Beta.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Beta.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Beta.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Additional documentation from Beta:

Note that the argument x must be a non-negative floating point tensor whose shape can be broadcast with self.a and self.b. For fixed leading dimensions, the last dimension represents counts for the corresponding Beta distribution in self.a and self.b. x is only legal if 0 < x < 1.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Beta.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Beta.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Beta.std(name='std')

Standard deviation.

tf.contrib.distributions.Beta.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Beta.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Beta.variance(name='variance')

Variance.

class tf.contrib.distributions.BetaWithSoftplusAB

Beta with softplus transform on a and b.

tf.contrib.distributions.BetaWithSoftplusAB.__init__(a, b, validate_args=False, allow_nan_stats=True, name='BetaWithSoftplusAB')

tf.contrib.distributions.BetaWithSoftplusAB.a

Shape parameter.

tf.contrib.distributions.BetaWithSoftplusAB.a_b_sum

Sum of parameters.

tf.contrib.distributions.BetaWithSoftplusAB.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.BetaWithSoftplusAB.b

Shape parameter.

tf.contrib.distributions.BetaWithSoftplusAB.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.BetaWithSoftplusAB.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BetaWithSoftplusAB.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.BetaWithSoftplusAB.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.BetaWithSoftplusAB.event_shape(name='event_shape')

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.BetaWithSoftplusAB.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.BetaWithSoftplusAB.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.BetaWithSoftplusAB.is_continuous

tf.contrib.distributions.BetaWithSoftplusAB.is_reparameterized

tf.contrib.distributions.BetaWithSoftplusAB.log_cdf(value, name='log_cdf')

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:

Note that the argument x must be a non-negative floating point tensor whose shape can be broadcast with self.a and self.b. For fixed leading dimensions, the last dimension represents counts for the corresponding Beta distribution in self.a and self.b. x is only legal if 0 < x < 1.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BetaWithSoftplusAB.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.BetaWithSoftplusAB.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.BetaWithSoftplusAB.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BetaWithSoftplusAB.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.BetaWithSoftplusAB.mean(name='mean')

Mean.

tf.contrib.distributions.BetaWithSoftplusAB.mode(name='mode')

Mode.

Additional documentation from Beta:

Note that the mode for the Beta distribution is only defined when a > 1, b > 1. This returns the mode when a > 1 and b > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.BetaWithSoftplusAB.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.BetaWithSoftplusAB.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.BetaWithSoftplusAB.param_static_shapes(cls, sample_shape)

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

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.BetaWithSoftplusAB.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.BetaWithSoftplusAB.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.BetaWithSoftplusAB.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.BetaWithSoftplusAB.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Additional documentation from Beta:

Note that the argument x must be a non-negative floating point tensor whose shape can be broadcast with self.a and self.b. For fixed leading dimensions, the last dimension represents counts for the corresponding Beta distribution in self.a and self.b. x is only legal if 0 < x < 1.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.BetaWithSoftplusAB.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.BetaWithSoftplusAB.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.BetaWithSoftplusAB.std(name='std')

Standard deviation.

tf.contrib.distributions.BetaWithSoftplusAB.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.BetaWithSoftplusAB.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.BetaWithSoftplusAB.variance(name='variance')

Variance.

class tf.contrib.distributions.Categorical

Categorical distribution.

The categorical distribution is parameterized by the log-probabilities of a set of classes.

tf.contrib.distributions.Categorical.__init__(logits, dtype=tf.int32, validate_args=False, allow_nan_stats=True, name='Categorical')

Initialize Categorical distributions using class log-probabilities.

Args:

• 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 indexes into the classes.
• dtype: The type of the event samples (default: int32).
• validate_args: Unused in this distribution.
• 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.
• name: A name for this distribution (optional).

tf.contrib.distributions.Categorical.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Categorical.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Categorical.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Categorical.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Categorical.entropy(name='entropy')

Shanon entropy in nats.

tf.contrib.distributions.Categorical.event_shape(name='event_shape')

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.Categorical.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Categorical.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Categorical.is_continuous

tf.contrib.distributions.Categorical.is_reparameterized

tf.contrib.distributions.Categorical.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Categorical.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Categorical.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Categorical.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Categorical.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Categorical.logits

tf.contrib.distributions.Categorical.mean(name='mean')

Mean.

tf.contrib.distributions.Categorical.mode(name='mode')

Mode.

tf.contrib.distributions.Categorical.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Categorical.num_classes

Scalar int32 tensor: the number of classes.

tf.contrib.distributions.Categorical.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Categorical.param_static_shapes(cls, sample_shape)

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

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.Categorical.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Categorical.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Categorical.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Categorical.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Categorical.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Categorical.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Categorical.std(name='std')

Standard deviation.

tf.contrib.distributions.Categorical.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Categorical.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Categorical.variance(name='variance')

Variance.

class tf.contrib.distributions.Chi2

The Chi2 distribution with degrees of freedom df.

The PDF of this distribution is:

pdf(x) = (x^(df/2 - 1)e^(-x/2))/(2^(df/2)Gamma(df/2)), x > 0

Note that the Chi2 distribution is a special case of the Gamma distribution, with Chi2(df) = Gamma(df/2, 1/2).

tf.contrib.distributions.Chi2.__init__(df, validate_args=False, allow_nan_stats=True, name='Chi2')

Construct Chi2 distributions with parameter df.

Args:

• df: Floating point tensor, the degrees of freedom of the distribution(s). df must contain only positive values.
• validate_args: Boolean, default False. Whether to assert that df > 0, and that x > 0 in the methods prob(x) and log_prob(x). If validate_args is False and the inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prepend to all ops created by this distribution.

tf.contrib.distributions.Chi2.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Chi2.alpha

Shape parameter.

tf.contrib.distributions.Chi2.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Chi2.beta

Inverse scale parameter.

tf.contrib.distributions.Chi2.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2.df

tf.contrib.distributions.Chi2.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Chi2.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.Chi2.event_shape(name='event_shape')

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.Chi2.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Chi2.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Chi2.is_continuous

tf.contrib.distributions.Chi2.is_reparameterized

tf.contrib.distributions.Chi2.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Chi2.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Chi2.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2.mean(name='mean')

Mean.

tf.contrib.distributions.Chi2.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.Chi2.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Chi2.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Chi2.param_static_shapes(cls, sample_shape)

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

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.Chi2.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Chi2.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Chi2.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Chi2.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Chi2.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Chi2.std(name='std')

Standard deviation.

tf.contrib.distributions.Chi2.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Chi2.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Chi2.variance(name='variance')

Variance.

class tf.contrib.distributions.Chi2WithAbsDf

Chi2 with parameter transform df = floor(abs(df)).

tf.contrib.distributions.Chi2WithAbsDf.__init__(df, validate_args=False, allow_nan_stats=True, name='Chi2WithAbsDf')

tf.contrib.distributions.Chi2WithAbsDf.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Chi2WithAbsDf.alpha

Shape parameter.

tf.contrib.distributions.Chi2WithAbsDf.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Chi2WithAbsDf.beta

Inverse scale parameter.

tf.contrib.distributions.Chi2WithAbsDf.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2WithAbsDf.df

tf.contrib.distributions.Chi2WithAbsDf.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Chi2WithAbsDf.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.Chi2WithAbsDf.event_shape(name='event_shape')

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.Chi2WithAbsDf.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Chi2WithAbsDf.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Chi2WithAbsDf.is_continuous

tf.contrib.distributions.Chi2WithAbsDf.is_reparameterized

tf.contrib.distributions.Chi2WithAbsDf.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2WithAbsDf.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Chi2WithAbsDf.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Chi2WithAbsDf.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2WithAbsDf.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2WithAbsDf.mean(name='mean')

Mean.

tf.contrib.distributions.Chi2WithAbsDf.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.Chi2WithAbsDf.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Chi2WithAbsDf.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Chi2WithAbsDf.param_static_shapes(cls, sample_shape)

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

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.Chi2WithAbsDf.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Chi2WithAbsDf.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Chi2WithAbsDf.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Chi2WithAbsDf.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Chi2WithAbsDf.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Chi2WithAbsDf.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Chi2WithAbsDf.std(name='std')

Standard deviation.

tf.contrib.distributions.Chi2WithAbsDf.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Chi2WithAbsDf.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Chi2WithAbsDf.variance(name='variance')

Variance.

class tf.contrib.distributions.Exponential

The Exponential distribution with rate parameter lam.

The PDF of this distribution is:

prob(x) = (lam * e^(-lam * x)), x > 0

Note that the Exponential distribution is a special case of the Gamma distribution, with Exponential(lam) = Gamma(1, lam).

tf.contrib.distributions.Exponential.__init__(lam, validate_args=False, allow_nan_stats=True, name='Exponential')

Construct Exponential distribution with parameter lam.

Args:

• lam: Floating point tensor, the rate of the distribution(s). lam must contain only positive values.
• validate_args: Boolean, default False. Whether to assert that lam > 0, and that x > 0 in the methods prob(x) and log_prob(x). If validate_args is False and the inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prepend to all ops created by this distribution.

tf.contrib.distributions.Exponential.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Exponential.alpha

Shape parameter.

tf.contrib.distributions.Exponential.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Exponential.beta

Inverse scale parameter.

tf.contrib.distributions.Exponential.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Exponential.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Exponential.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.Exponential.event_shape(name='event_shape')

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.Exponential.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Exponential.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Exponential.is_continuous

tf.contrib.distributions.Exponential.is_reparameterized

tf.contrib.distributions.Exponential.lam

tf.contrib.distributions.Exponential.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Exponential.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Exponential.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Exponential.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Exponential.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Exponential.mean(name='mean')

Mean.

tf.contrib.distributions.Exponential.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.Exponential.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Exponential.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Exponential.param_static_shapes(cls, sample_shape)

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

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.Exponential.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Exponential.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Exponential.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Exponential.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Exponential.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Exponential.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Exponential.std(name='std')

Standard deviation.

tf.contrib.distributions.Exponential.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Exponential.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Exponential.variance(name='variance')

Variance.

class tf.contrib.distributions.ExponentialWithSoftplusLam

Exponential with softplus transform on lam.

tf.contrib.distributions.ExponentialWithSoftplusLam.__init__(lam, validate_args=False, allow_nan_stats=True, name='ExponentialWithSoftplusLam')

tf.contrib.distributions.ExponentialWithSoftplusLam.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.ExponentialWithSoftplusLam.alpha

Shape parameter.

tf.contrib.distributions.ExponentialWithSoftplusLam.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.ExponentialWithSoftplusLam.beta

Inverse scale parameter.

tf.contrib.distributions.ExponentialWithSoftplusLam.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.ExponentialWithSoftplusLam.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.ExponentialWithSoftplusLam.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.ExponentialWithSoftplusLam.event_shape(name='event_shape')

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.ExponentialWithSoftplusLam.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.ExponentialWithSoftplusLam.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.ExponentialWithSoftplusLam.is_continuous

tf.contrib.distributions.ExponentialWithSoftplusLam.is_reparameterized

tf.contrib.distributions.ExponentialWithSoftplusLam.lam

tf.contrib.distributions.ExponentialWithSoftplusLam.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.ExponentialWithSoftplusLam.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.ExponentialWithSoftplusLam.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.ExponentialWithSoftplusLam.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.ExponentialWithSoftplusLam.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.ExponentialWithSoftplusLam.mean(name='mean')

Mean.

tf.contrib.distributions.ExponentialWithSoftplusLam.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.ExponentialWithSoftplusLam.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.ExponentialWithSoftplusLam.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.ExponentialWithSoftplusLam.param_static_shapes(cls, sample_shape)

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

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.ExponentialWithSoftplusLam.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.ExponentialWithSoftplusLam.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.ExponentialWithSoftplusLam.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.ExponentialWithSoftplusLam.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.ExponentialWithSoftplusLam.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.ExponentialWithSoftplusLam.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.ExponentialWithSoftplusLam.std(name='std')

Standard deviation.

tf.contrib.distributions.ExponentialWithSoftplusLam.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.ExponentialWithSoftplusLam.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.ExponentialWithSoftplusLam.variance(name='variance')

Variance.

class tf.contrib.distributions.Gamma

The Gamma distribution with parameter alpha and beta.

The parameters are the shape and inverse scale parameters alpha, beta.

The PDF of this distribution is:

pdf(x) = (beta^alpha)(x^(alpha-1))e^(-x*beta)/Gamma(alpha), x > 0

and the CDF of this distribution is:

cdf(x) = GammaInc(alpha, beta * x) / Gamma(alpha), x > 0

where GammaInc is the incomplete lower Gamma function.

WARNING: This distribution may draw 0-valued samples for small alpha values. See the note on tf.random_gamma.

Examples:

dist = Gamma(alpha=3.0, beta=2.0)
dist2 = Gamma(alpha=[3.0, 4.0], beta=[2.0, 3.0])

tf.contrib.distributions.Gamma.__init__(alpha, beta, validate_args=False, allow_nan_stats=True, name='Gamma')

Construct Gamma distributions with parameters alpha and beta.

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

Args:

• alpha: Floating point tensor, the shape params of the distribution(s). alpha must contain only positive values.
• beta: Floating point tensor, the inverse scale params of the distribution(s). beta must contain only positive values.
• validate_args: Boolean, default False. Whether to assert that a > 0, b > 0, and that x > 0 in the methods prob(x) and log_prob(x). If validate_args is False and the inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prepend to all ops created by this distribution.

Raises:

• TypeError: if alpha and beta are different dtypes.

tf.contrib.distributions.Gamma.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.Gamma.alpha

Shape parameter.

tf.contrib.distributions.Gamma.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.Gamma.beta

Inverse scale parameter.

tf.contrib.distributions.Gamma.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Gamma.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.Gamma.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.Gamma.event_shape(name='event_shape')

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.Gamma.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Gamma.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.Gamma.is_continuous

tf.contrib.distributions.Gamma.is_reparameterized

tf.contrib.distributions.Gamma.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Gamma.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Gamma.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Gamma.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Gamma.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.Gamma.mean(name='mean')

Mean.

tf.contrib.distributions.Gamma.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.Gamma.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.Gamma.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.Gamma.param_static_shapes(cls, sample_shape)

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

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.Gamma.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.Gamma.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.Gamma.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.Gamma.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.Gamma.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.Gamma.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.Gamma.std(name='std')

Standard deviation.

tf.contrib.distributions.Gamma.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.Gamma.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.Gamma.variance(name='variance')

Variance.

class tf.contrib.distributions.GammaWithSoftplusAlphaBeta

Gamma with softplus transform on alpha and beta.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.__init__(alpha, beta, validate_args=False, allow_nan_stats=True, name='GammaWithSoftplusAlphaBeta')

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.alpha

Shape parameter.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.beta

Inverse scale parameter.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from Gamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.event_shape(name='event_shape')

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.GammaWithSoftplusAlphaBeta.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.is_continuous

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.is_reparameterized

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.mean(name='mean')

Mean.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.mode(name='mode')

Mode.

Additional documentation from Gamma:

The mode of a gamma distribution is (alpha - 1) / beta when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.GammaWithSoftplusAlphaBeta.param_static_shapes(cls, sample_shape)

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

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.GammaWithSoftplusAlphaBeta.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from Gamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.std(name='std')

Standard deviation.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.GammaWithSoftplusAlphaBeta.variance(name='variance')

Variance.

class tf.contrib.distributions.InverseGamma

The InverseGamma distribution with parameter alpha and beta.

The parameters are the shape and inverse scale parameters alpha, beta.

The PDF of this distribution is:

pdf(x) = (beta^alpha)/Gamma(alpha)(x^(-alpha-1))e^(-beta/x), x > 0

and the CDF of this distribution is:

cdf(x) = GammaInc(alpha, beta / x) / Gamma(alpha), x > 0

where GammaInc is the upper incomplete Gamma function.

Examples:

dist = InverseGamma(alpha=3.0, beta=2.0)
dist2 = InverseGamma(alpha=[3.0, 4.0], beta=[2.0, 3.0])

tf.contrib.distributions.InverseGamma.__init__(alpha, beta, validate_args=False, allow_nan_stats=True, name='InverseGamma')

Construct InverseGamma distributions with parameters alpha and beta.

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

Args:

• alpha: Floating point tensor, the shape params of the distribution(s). alpha must contain only positive values.
• beta: Floating point tensor, the scale params of the distribution(s). beta must contain only positive values.
• validate_args: Boolean, default False. Whether to assert that a > 0, b > 0, and that x > 0 in the methods prob(x) and log_prob(x). If validate_args is False and the inputs are invalid, correct behavior is not guaranteed.
• 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.
• name: The name to prepend to all ops created by this distribution.

Raises:

• TypeError: if alpha and beta are different dtypes.

tf.contrib.distributions.InverseGamma.allow_nan_stats

Python boolean 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 boolean.

tf.contrib.distributions.InverseGamma.alpha

Shape parameter.

tf.contrib.distributions.InverseGamma.batch_shape(name='batch_shape')

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

The product of the dimensions of the batch_shape is the number of independent distributions of this kind the instance represents.

Args:

• name: name to give to the op

Returns:

• batch_shape: Tensor.

tf.contrib.distributions.InverseGamma.beta

Scale parameter.

tf.contrib.distributions.InverseGamma.cdf(value, name='cdf')

Cumulative distribution function.

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

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

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.InverseGamma.dtype

The DType of Tensors handled by this Distribution.

tf.contrib.distributions.InverseGamma.entropy(name='entropy')

Shanon entropy in nats.

Additional documentation from InverseGamma:

This is defined to be

entropy = alpha - log(beta) + log(Gamma(alpha))
+ (1-alpha)digamma(alpha)

where digamma(alpha) is the digamma function.

tf.contrib.distributions.InverseGamma.event_shape(name='event_shape')

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.InverseGamma.get_batch_shape()

Shape of a single sample from a single event index as a TensorShape.

Same meaning as batch_shape. May be only partially defined.

Returns:

• batch_shape: TensorShape, possibly unknown.

tf.contrib.distributions.InverseGamma.get_event_shape()

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

Same meaning as event_shape. May be only partially defined.

Returns:

• event_shape: TensorShape, possibly unknown.

tf.contrib.distributions.InverseGamma.is_continuous

tf.contrib.distributions.InverseGamma.is_reparameterized

tf.contrib.distributions.InverseGamma.log_cdf(value, name='log_cdf')

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.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.InverseGamma.log_pdf(value, name='log_pdf')

Log probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.InverseGamma.log_pmf(value, name='log_pmf')

Log probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.InverseGamma.log_prob(value, name='log_prob')

Log probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.InverseGamma.log_survival_function(value, name='log_survival_function')

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: The name to give this op.

Returns:

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

tf.contrib.distributions.InverseGamma.mean(name='mean')

Mean.

Additional documentation from InverseGamma:

The mean of an inverse gamma distribution is beta / (alpha - 1), when alpha > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN

tf.contrib.distributions.InverseGamma.mode(name='mode')

Mode.

Additional documentation from InverseGamma:

The mode of an inverse gamma distribution is beta / (alpha + 1).

tf.contrib.distributions.InverseGamma.name

Name prepended to all ops created by this Distribution.

tf.contrib.distributions.InverseGamma.param_shapes(cls, sample_shape, name='DistributionParamShapes')

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

Subclasses should override static 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.InverseGamma.param_static_shapes(cls, sample_shape)

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

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.InverseGamma.parameters

Dictionary of parameters used by this Distribution.

tf.contrib.distributions.InverseGamma.pdf(value, name='pdf')

Probability density function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if not is_continuous.

tf.contrib.distributions.InverseGamma.pmf(value, name='pmf')

Probability mass function.

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

Raises:

• TypeError: if is_continuous.

tf.contrib.distributions.InverseGamma.prob(value, name='prob')

Probability density/mass function (depending on is_continuous).

Args:

• value: float or double Tensor.
• name: The name to give this op.

Returns:

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

tf.contrib.distributions.InverseGamma.sample(sample_shape=(), seed=None, name='sample')

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: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with prepended dimensions sample_shape.

tf.contrib.distributions.InverseGamma.sample_n(n, seed=None, name='sample_n')

Generate n samples.

Additional documentation from InverseGamma:

See the documentation for tf.random_gamma for more details.

Args:

• n: Scalar Tensor of type int32 or int64, the number of observations to sample.
• seed: Python integer seed for RNG
• name: name to give to the op.

Returns:

• samples: a Tensor with a prepended dimension (n,).

Raises:

• TypeError: if n is not an integer type.

tf.contrib.distributions.InverseGamma.std(name='std')

Standard deviation.

tf.contrib.distributions.InverseGamma.survival_function(value, name='survival_function')

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: The name to give this op.

Returns:

Tensorof shapesample_shape(x) + self.batch_shapewith values of typeself.dtype`.

tf.contrib.distributions.InverseGamma.validate_args

Python boolean indicated possibly expensive checks are enabled.

tf.contrib.distributions.InverseGamma.variance(name='variance')

Variance.

Additional documentation from InverseGamma:

Variance for inverse gamma is defined only for alpha > 2. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN.

class tf.contrib.distributions.InverseGammaWithSoftplusAlphaBeta

Inverse Gamma with softplus applied to alpha and beta.

tf.contrib.distributions.InverseGammaWithSoftplusAlphaBeta.__init__(alpha, beta, validate_args=False, allow_nan_stats=True, name='InverseGammaWithSoftplusAlphaBeta')