tfp.distributions.JointDistribution | TensorFlow Probability (original) (raw)

Joint distribution over one or more component distributions.

tfp.distributions.JointDistribution(
    dtype,
    validate_args,
    parameters,
    name,
    use_vectorized_map=False,
    batch_ndims=None,
    experimental_use_kahan_sum=False
)

This distribution enables both sampling and joint probability computation from a single model specification.

A joint distribution is a collection of possibly interdependent distributions.

Subclass Requirements

Subclasses implement:

_model_coroutine: A generator that yields a sequence oftfd.Distribution-like instances.
_model_flatten: takes a structured input and returns a sequence. The sequence order must match the order distributions are yielded from_model_coroutine.
_model_unflatten: takes a sequence and returns a structure matching the semantics of the JointDistribution subclass.

Args
dtype	The type of the event samples. None implies no type-enforcement.
reparameterization_type	Instance of ReparameterizationType. If tfd.FULLY_REPARAMETERIZED, then samples from the distribution are fully reparameterized, and straight-through gradients are supported. If tfd.NOT_REPARAMETERIZED, then samples from the distribution are not fully reparameterized, and straight-through gradients are either partially unsupported or are not supported at all.
validate_args	Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats	Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
parameters	Python dict of parameters used to instantiate thisDistribution.
graph_parents	Python list of graph prerequisites of thisDistribution.
name	Python str name prefixed to Ops created by this class. Default: subclass name.

Raises
ValueError	if any member of graph_parents is None or not a Tensor.

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_ndims
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	Indicates whether part distributions have 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.
parameters	Dictionary of parameters used to instantiate this Distribution.
reparameterization_type	Describes how samples from the distribution are reparameterized.Currently this is one of the static instancestfd.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.
use_vectorized_map
validate_args	Python bool indicating possibly expensive checks are enabled.
variables	Sequence of variables owned by this module and its submodules.

Child Classes

class Root

Methods

`batch_shape_tensor`

View source

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`

View source

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`

View source

copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

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

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

`covariance`

View source

covariance(
    name='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 Edenotes 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 andk' = reduce_prod(self.event_shape).

`cross_entropy`

View source

cross_entropy(
    other, name='cross_entropy'
)

Computes the (Shannon) cross entropy.

Denote this distribution (self) by P and the other distribution byQ. 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`

View source

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

Shannon entropy in nats.

`event_shape_tensor`

View source

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.

`experimental_default_event_space_bijector`

View source

experimental_default_event_space_bijector(
    *args, **kwargs
)

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

Distributions with continuous support may implement_default_event_space_bijector which returns a subclass oftfp.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 theCholeskyLKJ distribution is tfp.bijectors.CorrelationCholesky, which maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal.

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

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

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

Returns
event_space_bijector	Bijector instance or None.

`experimental_fit`

View source

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

Instantiates a distribution that maximizes the likelihood of x.

Args
value	a Tensor valid sample from this distribution family.
sample_ndims	Positive int Tensor number of leftmost dimensions ofvalue 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 tocls.__init__. These take precedence in case of collision with the fitted parameters; for example,tfd.Normal.experimental_fit([1., 1.], scale=20.) returns a Normal distribution with scale=20. rather than the maximum likelihood parameter scale=0..

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

`experimental_local_measure`

View source

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

Returns a log probability density together with a TangentSpace.

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

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

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

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

`experimental_pin`

View source

experimental_pin(
    *args, **kwargs
)

Pins some parts, returning an unnormalized distribution object.

The calling convention is much like other JointDistribution methods (e.g.log_prob), but with the difference that not all parts are required. In this respect, the behavior is similar to that of the sample function'svalue argument.

Examples:

# Given the following joint distribution:
jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1., name='z'),
    tfd.Normal(0., 1., name='y'),
    lambda y, z: tfd.Normal(y + z, 1., name='x')
], validate_args=True)

# The following calls are all permissible and produce
# `JointDistributionPinned` objects behaving identically.
PartialXY = collections.namedtuple('PartialXY', 'x,y')
PartialX = collections.namedtuple('PartialX', 'x')
assert (jd.experimental_pin(x=2.).pins ==
        jd.experimental_pin(x=2., z=None).pins ==
        jd.experimental_pin(dict(x=2.)).pins ==
        jd.experimental_pin(dict(x=2., y=None)).pins ==
        jd.experimental_pin(PartialXY(x=2., y=None)).pins ==
        jd.experimental_pin(PartialX(x=2.)).pins ==
        jd.experimental_pin(None, None, 2.).pins ==
        jd.experimental_pin([None, None, 2.]).pins)

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

Returns
pinned	a tfp.experimental.distributions.JointDistributionPinned with the given values pinned.

`experimental_sample_and_log_prob`

View source

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.

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

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

`is_scalar_batch`

View source

is_scalar_batch(
    name='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 for each distribution in model.

`is_scalar_event`

View source

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 for each distribution in model.

`kl_divergence`

View source

kl_divergence(
    other, name='kl_divergence'
)

Computes the Kullback--Leibler divergence.

Denote this distribution (self) by p and the other distribution byq. 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`

View source

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 whenx << -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`

View source

log_prob(
    *args, **kwargs
)

Log probability density/mass function.

The measure methods of JointDistribution (log_prob, prob, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.log_prob(sample) ==
        jd.log_prob(value=sample) ==
        jd.log_prob(z, x) ==
        jd.log_prob(z=z, x=x) ==
        jd.log_prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.log_prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.log_prob(**sample)

JointDistribution component distributions names are resolved viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (see subclass documentation for details). Generally, for components where a name was provided--- either explicitly as the name argument to a distribution or as a key in a dict-valued JointDistribution, or implicitly, e.g., by the argument name of a JointDistributionSequential distribution-making function---the provided name will be used. Otherwise the component will receive a dummy name; these may change without warning and should not be relied upon.

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.log_prob([4.])
# ==> Tensor with shape `[]`.
lp = trivial_jd.log_prob(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of log_probs---we could instead writetrivial_jd.log_prob(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

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

`log_prob_parts`

View source

log_prob_parts(
    *args, **kwargs
)

Log probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.log_prob_parts(sample) ==
        jd.log_prob_parts(value=sample) ==
        jd.log_prob_parts(z, x) ==
        jd.log_prob_parts(z=z, x=x) ==
        jd.log_prob_parts(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.log_prob_parts(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.log_prob_parts([4.])
# ==> Tensor with shape `[]`.
lp_parts = trivial_jd.log_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of log_prob_partss---we could instead writetrivial_jd.log_prob_parts(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

Returns
log_prob_parts	a self.dtype-like structure of Tensors representing the log_prob for each component distribution evaluated at each corresponding value.

`log_survival_function`

View source

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 typeself.dtype.

`mean`

View source

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

Mean.

`mode`

View source

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

Mode.

`param_shapes`

View source

@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.

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

Returns
dict of parameter name to Tensor shapes.

`param_static_shapes`

View source

@classmethod param_static_shapes( sample_shape )

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

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

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

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

Returns
dict of parameter name to TensorShape.

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

`parameter_properties`

View source

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

Returns a dict mapping constructor arg names to property annotations.

This dict should include an entry for each of the distribution'sTensor-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 fromtf.vectorized_map.

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

Returns
parameter_properties	Astr ->tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names toParameterProperties` instances.

Raises
NotImplementedError	if the distribution class does not implement_parameter_properties.

`prob`

View source

prob(
    *args, **kwargs
)

Probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.prob(sample) ==
        jd.prob(value=sample) ==
        jd.prob(z, x) ==
        jd.prob(z=z, x=x) ==
        jd.prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.prob(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.prob([4.])
# ==> Tensor with shape `[]`.
prob = trivial_jd.prob(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of probs---we could instead writetrivial_jd.prob(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

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

`prob_parts`

View source

prob_parts(
    *args, **kwargs
)

Probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.prob_parts(sample) ==
        jd.prob_parts(value=sample) ==
        jd.prob_parts(z, x) ==
        jd.prob_parts(z=z, x=x) ==
        jd.prob_parts(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.prob_parts(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.prob_parts([4.])
# ==> Tensor with shape `[]`.
p_parts = trivial_jd.prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of prob_partss---we could instead writetrivial_jd.prob_parts(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

Returns
prob_parts	a self.dtype-like structure of Tensors representing theprob for each component distribution evaluated at each correspondingvalue.

`quantile`

View source

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`

View source

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.

Additional documentation from JointDistribution:

`kwargs`:

value: Tensors structured like type(model) used to parameterize other dependent ("downstream") distribution-making functions. Using None for any element will trigger a sample from the corresponding distribution. Default value: None (i.e., draw a sample from each distribution).

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

Returns
samples	a Tensor with prepended dimensions sample_shape.

`sample_distributions`

View source

sample_distributions(
    sample_shape=(),
    seed=None,
    value=None,
    name='sample_distributions',
    **kwargs
)

Generate samples and the (random) distributions.

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

Args
sample_shape	0D or 1D int32 Tensor. Shape of the generated samples.
seed	PRNG seed; see tfp.random.sanitize_seed for details.
value	list of Tensors in distribution_fn order to use to parameterize other ("downstream") distribution makers. Default value: None (i.e., draw a sample from each distribution).
name	name prepended to ops created by this function. Default value: "sample_distributions".
**kwargs	This is an alternative to passing a value, and achieves the same effect. Named arguments will be used to parameterize other dependent ("downstream") distribution-making functions. If a valueargument is also provided, raises a ValueError.

Returns
distributions	a tuple of Distribution instances for each ofdistribution_fn.
samples	a tuple of Tensors with prepended dimensions sample_shapefor each of distribution_fn.

`stddev`

View source

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, Edenotes 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 tobatch_shape + event_shape, i.e., the same shape as self.mean().

`survival_function`

View source

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 typeself.dtype.

`unnormalized_log_prob`

View source

unnormalized_log_prob(
    *args, **kwargs
)

Unnormalized log probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_log_prob(sample) ==
        jd.unnormalized_log_prob(value=sample) ==
        jd.unnormalized_log_prob(z, x) ==
        jd.unnormalized_log_prob(z=z, x=x) ==
        jd.unnormalized_log_prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_log_prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_log_prob(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.unnormalized_log_prob([4.])
# ==> Tensor with shape `[]`.
lp = trivial_jd.unnormalized_log_prob(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of unnormalized_log_probs---we could instead writetrivial_jd.unnormalized_log_prob(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

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

`unnormalized_log_prob_parts`

View source

unnormalized_log_prob_parts(
    *args, **kwargs
)

Unnormalized log probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_log_prob_parts(sample) ==
        jd.unnormalized_log_prob_parts(value=sample) ==
        jd.unnormalized_log_prob_parts(z, x) ==
        jd.unnormalized_log_prob_parts(z=z, x=x) ==
        jd.unnormalized_log_prob_parts(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_log_prob_parts(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.unnormalized_log_prob_parts([4.])
# ==> Tensor with shape `[]`.
unnorm_lp_parts = trivial_jd.unnormalized_log_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of unnormalized_log_prob_partss---we could instead writetrivial_jd.unnormalized_log_prob_parts(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

Returns
unnormalized_log_prob_parts	a self.dtype-like structure of Tensors representing the unnormalized_log_prob for each component distribution evaluated at each corresponding value.

`unnormalized_prob_parts`

View source

unnormalized_prob_parts(
    *args, **kwargs
)

Unnormalized probability density/mass function.

jd = tfd.JointDistributionSequential([
    tfd.Normal(0., 1.),
    lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_prob_parts(sample) ==
        jd.unnormalized_prob_parts(value=sample) ==
        jd.unnormalized_prob_parts(z, x) ==
        jd.unnormalized_prob_parts(z=z, x=x) ==
        jd.unnormalized_prob_parts(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_prob_parts(**sample)

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.unnormalized_prob_parts([4.])
# ==> Tensor with shape `[]`.
unnorm_prob_parts = trivial_jd.unnormalized_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of unnormalized_prob_partss---we could instead writetrivial_jd.unnormalized_prob_parts(np.array([4])).

Args
*args	Positional arguments: a value structure or component values (see above).
**kwargs	Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method.

Returns
unnormalized_prob_parts	a self.dtype-like structure of Tensors representing the unnormalized_prob for each component distribution evaluated at each corresponding value.

`variance`

View source

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, Edenotes 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 tobatch_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)>

Args
method	The method to wrap.

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

`getitem`

View source

__getitem__(
    slices
)

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

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

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

Args
slices	slices from the [] operator

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

`iter`

View source

__iter__()

tfp.distributions.JointDistribution | TensorFlow Probability (original) (raw)

Subclass Requirements

Subclasses implement:

Child Classes

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

experimental_default_event_space_bijector

experimental_fit

experimental_local_measure

experimental_pin

Examples:

experimental_sample_and_log_prob

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_prob_parts

log_survival_function

mean

mode

param_shapes

param_static_shapes

parameter_properties

prob

prob_parts

quantile

sample

kwargs:

sample_distributions

stddev

survival_function

unnormalized_log_prob

unnormalized_log_prob_parts

unnormalized_prob_parts

variance

with_name_scope

__getitem__

__iter__

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`experimental_default_event_space_bijector`

`experimental_fit`

`experimental_local_measure`

`experimental_pin`

`experimental_sample_and_log_prob`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_prob_parts`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`parameter_properties`

`prob`

`prob_parts`

`quantile`

`sample`

`kwargs`:

`sample_distributions`

`stddev`

`survival_function`

`unnormalized_log_prob`

`unnormalized_log_prob_parts`

`unnormalized_prob_parts`

`variance`

`with_name_scope`

`getitem`

`iter`