tfc.distributions.NoisyLogistic

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Logistic distribution with additive i.i.d. uniform noise.

Inherits From: UniformNoiseAdapter

tfc.distributions.NoisyLogistic(
    name='NoisyLogistic', **kwargs
)

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. base The base distribution (without uniform noise). batch_shape Shape of a single sample from a single event index as a TensorShape.

May be partially defined or unknown.

The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. dtype The DType of 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. experimental_shard_axis_names The list or structure of lists of active shard axis names. name Name prepended to all ops created by this Distribution. name_scope Returns a tf.name_scope instance for this class. non_trainable_variables Sequence of non-trainable variables owned by this module and its submodules.

Currently this is one of the static instances tfd.FULLY_REPARAMETERIZED or tfd.NOT_REPARAMETERIZED. submodules Sequence of all sub-modules.

Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).

a = tf.Module()
b = tf.Module()
c = tf.Module()
a.b = b
b.c = c
list(a.submodules) == [b, c]
True
list(b.submodules) == [c]
True
list(c.submodules) == []
True

trainable_variables Sequence of trainable variables owned by this module and its submodules.

Methods

batch_shape_tensor

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.

name name to give to the op

batch_shape Tensor.

cdf

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

Cumulative distribution function.

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

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

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

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

copy

copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

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

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

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.

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

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

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.

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

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

entropy

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

Shannon entropy in nats.

event_shape_tensor

event_shape_tensor(
    name='event_shape_tensor'
)

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

name name to give to the op

event_shape Tensor.

experimental_default_event_space_bijector

experimental_default_event_space_bijector(
    *args, **kwargs
)

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

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

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

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

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

event_space_bijector Bijector instance or None.

experimental_fit

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

Instantiates a distribution that maximizes the likelihood of x.

value a Tensor valid sample from this distribution family. sample_ndims Positive int Tensor number of leftmost dimensions of value that index i.i.d. samples. Default value: 1. validate_args Python bool, default False. When True, distribution parameters are checked for validity despite possibly degrading runtime performance. When False, invalid inputs may silently render incorrect outputs. Default value: False. **init_kwargs Additional keyword arguments passed through to cls.__init__. These take precedence in case of collision with the fitted parameters; for example, tfd.Normal.experimental_fit([1., 1.], scale=20.) returns a Normal distribution with scale=20. rather than the maximum likelihood parameter scale=0..

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

experimental_local_measure

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

Returns a log probability density together with a TangentSpace.

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

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

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

experimental_sample_and_log_prob

experimental_sample_and_log_prob(
    sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
)

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

The default implementation simply calls sample and log_prob:

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

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

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

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

is_scalar_batch

is_scalar_batch(
    name='is_scalar_batch'
)

Indicates that batch_shape == [].

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

is_scalar_batch bool scalar Tensor.

is_scalar_event

is_scalar_event(
    name='is_scalar_event'
)

Indicates that event_shape == [].

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

is_scalar_event bool scalar Tensor.

kl_divergence

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.

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

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

log_cdf

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.

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

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

log_prob

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

Log probability density/mass function.

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

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

log_survival_function

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.

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

mean

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

Mean.

mode

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

Mode.

param_shapes

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

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

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

Subclasses should override class method _param_shapes.

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

param_static_shapes

@classmethod
param_static_shapes(
    sample_shape
)

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

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

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

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

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

parameter_properties

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

Returns a dict mapping constructor arg names to property annotations.

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

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

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

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

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

parameter_properties A str ->tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names toParameterProperties` instances.

NotImplementedError if the distribution class does not implement _parameter_properties.

prob

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

Probability density/mass function.

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

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

quantile

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

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

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

sample

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.

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

samples a Tensor with prepended dimensions sample_shape.

stddev

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.

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

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

survival_function

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).

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

unnormalized_log_prob

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

Potentially unnormalized log probability density/mass function.

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

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

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

variance

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.

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

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

with_name_scope

@classmethod
with_name_scope(
    method
)

Decorator to automatically enter the module name scope.

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

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

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

method The method to wrap.

__getitem__

__getitem__(
    slices
)

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

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

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

slices slices from the [] operator

dist A new tfd.Distribution instance with sliced parameters.

__iter__

__iter__()