tfp.substrates.numpy.distributions.RelaxedOneHotCategorical

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RelaxedOneHotCategorical distribution with temperature and logits.

Inherits From: TransformedDistribution

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Main aliases

tfp.experimental.substrates.numpy.distributions.RelaxedOneHotCategorical

tfp.substrates.numpy.distributions.RelaxedOneHotCategorical(
    temperature, logits=None, probs=None, validate_args=False, allow_nan_stats=True,
    name='RelaxedOneHotCategorical'
)

The RelaxedOneHotCategorical is a distribution over random probability vectors, vectors of positive real values that sum to one, which continuously approximates a OneHotCategorical. The degree of approximation is controlled by a temperature: as the temperature goes to 0 the RelaxedOneHotCategorical becomes discrete with a distribution described by the logits or probs parameters, as the temperature goes to infinity the RelaxedOneHotCategorical becomes the constant distribution that is identically the constant vector of (1/event_size, ..., 1/event_size).

The RelaxedOneHotCategorical distribution was concurrently introduced as the Gumbel-Softmax (Jang et al., 2016) and Concrete (Maddison et al., 2016) distributions for use as a reparameterized continuous approximation to the Categorical one-hot distribution. If you use this distribution, please cite both papers.

Examples

Creates a continuous distribution, which approximates a 3-class one-hot categorical distribution. The 2nd class is the most likely to be the largest component in samples drawn from this distribution.

temperature = 0.5
p = [0.1, 0.5, 0.4]
dist = RelaxedOneHotCategorical(temperature, probs=p)

Creates a continuous distribution, which approximates a 3-class one-hot categorical distribution. The 2nd class is the most likely to be the largest component in samples drawn from this distribution.

temperature = 0.5
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)

Creates a continuous distribution, which approximates a 3-class one-hot categorical distribution. Because the temperature is very low, samples from this distribution are almost discrete, with one component almost 1 and the others nearly 0. The 2nd class is the most likely to be the largest component in samples drawn from this distribution.

temperature = 1e-5
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)

Creates a continuous distribution, which approximates a 3-class one-hot categorical distribution. Because the temperature is very high, samples from this distribution are usually close to the (1/3, 1/3, 1/3) vector. The 2nd class is still the most likely to be the largest component in samples drawn from this distribution.

temperature = 10
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)

Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. 2016.

Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. 2016.

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

Attributes
allow_nan_stats	Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.
batch_shape	Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
bijector	Function transforming x => y.
distribution	Base distribution, p(x).
dtype	The DType of Tensors handled by this Distribution.
event_shape	Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.
event_size	Scalar int32 tensor: the number of classes.
logits	Input argument logits.
name	Name prepended to all ops created by this Distribution.
parameters	Dictionary of parameters used to instantiate this Distribution.
probs	Input argument probs.
reparameterization_type	Describes how samples from the distribution are reparameterized. Currently this is one of the static instances tfd.FULLY_REPARAMETERIZED or tfd.NOT_REPARAMETERIZED.
temperature	Batchwise temperature tensor of a RelaxedCategorical.
trainable_variables
validate_args	Python bool indicating possibly expensive checks are enabled.
variables

Methods

batch_shape_tensor

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batch_shape_tensor(
    name='batch_shape_tensor'
)

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

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

Args
name	name to give to the op

Returns
batch_shape	Tensor.

cdf

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cdf(
    value, name='cdf', **kwargs
)

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

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

copy

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copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

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

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

covariance

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covariance(
    name='covariance', **kwargs
)

Covariance.

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

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

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

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

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

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

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

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

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

cross_entropy

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cross_entropy(
    other, name='cross_entropy'
)

Computes the (Shannon) cross entropy.

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

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

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

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

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

entropy

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entropy(
    name='entropy', **kwargs
)

Shannon entropy in nats.

event_shape_tensor

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event_shape_tensor(
    name='event_shape_tensor'
)

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

Args
name	name to give to the op

Returns
event_shape	Tensor.

is_scalar_batch

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is_scalar_batch(
    name='is_scalar_batch'
)

Indicates that batch_shape == [].

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

Returns
is_scalar_batch	bool scalar Tensor.

is_scalar_event

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is_scalar_event(
    name='is_scalar_event'
)

Indicates that event_shape == [].

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

Returns
is_scalar_event	bool scalar Tensor.

kl_divergence

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kl_divergence(
    other, name='kl_divergence'
)

Computes the Kullback--Leibler divergence.

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

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

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

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

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

log_cdf

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log_cdf(
    value, name='log_cdf', **kwargs
)

Log cumulative distribution function.

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

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

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

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

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

log_prob

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log_prob(
    value, name='log_prob', **kwargs
)

Log probability density/mass function.

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

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

log_survival_function

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log_survival_function(
    value, name='log_survival_function', **kwargs
)

Log survival function.

Given random variable X, the survival function is defined:

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

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

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

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

logits_parameter

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logits_parameter(
    name=None
)

Logits vec computed from non-None input arg (probs or logits).

mean

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mean(
    name='mean', **kwargs
)

Mean.

mode

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mode(
    name='mode', **kwargs
)

Mode.

param_shapes

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@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)

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

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

Subclasses should override class method _param_shapes.

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

Returns
dict of parameter name to Tensor shapes.

param_static_shapes

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@classmethod
param_static_shapes(
    sample_shape
)

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

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

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

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

Returns
dict of parameter name to TensorShape.

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

prob

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prob(
    value, name='prob', **kwargs
)

Probability density/mass function.

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

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

probs_parameter

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probs_parameter(
    name=None
)

Probs vec computed from non-None input arg (probs or logits).

quantile

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quantile(
    value, name='quantile', **kwargs
)

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

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

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

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

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

sample

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sample(
    sample_shape=(), seed=None, name='sample', **kwargs
)

Generate samples of the specified shape.

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

Args
sample_shape	0D or 1D int32 Tensor. Shape of the generated samples.
seed	Python integer or tfp.util.SeedStream instance, for seeding PRNG.
name	name to give to the op.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
samples	a Tensor with prepended dimensions sample_shape.

stddev

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stddev(
    name='stddev', **kwargs
)

Standard deviation.

Standard deviation is defined as,

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

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

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

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

survival_function

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survival_function(
    value, name='survival_function', **kwargs
)

Survival function.

Given random variable X, the survival function is defined:

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

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

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

variance

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variance(
    name='variance', **kwargs
)

Variance.

Variance is defined as,

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

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

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

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

__getitem__

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__getitem__(
    slices
)

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

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

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

Args
slices	slices from the [] operator

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

__iter__

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__iter__()