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Joint distribution over one or more component distributions.
Inherits From: Distribution
tfp.substrates.numpy.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 theJointDistribution
subclass.
Raises | |
---|---|
ValueError
|
if any member of graph_parents is None or not a Tensor .
|
Child Classes
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.
Args | |
---|---|
name
|
name to give to the op |
Returns | |
---|---|
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]
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
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
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
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
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
.
Args | |
---|---|
name
|
name to give to the op |
Returns | |
---|---|
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 | |
---|---|
*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
@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 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. .
|
Returns | |
---|---|
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.
Args | |
---|---|
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. |
Returns | |
---|---|
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 .
|
Raises | |
---|---|
UnspecifiedTangentSpaceError if backward_compat is False and
the _experimental_tangent_space attribute has not been defined.
|
experimental_pin
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's
value
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
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 Tensor s, 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 == []
.
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
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
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
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
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 via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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_prob
s---we could instead write
trivial_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
log_prob_parts(
*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_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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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_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_parts
s---we could instead write
trivial_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 Tensor s representing
the log_prob for each component distribution evaluated at each
corresponding value .
|
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
.
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 .
|
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()
.
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
@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.
|
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
.
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
|
A
str -> tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names to ParameterProperties`
instances.
|
Raises | |
---|---|
NotImplementedError
|
if the distribution class does not implement
_parameter_properties .
|
prob
prob(
*args, **kwargs
)
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.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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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.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 prob
s---we could instead write
trivial_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
prob_parts(
*args, **kwargs
)
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.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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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.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_parts
s---we could instead write
trivial_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 Tensor s representing the
prob for each component distribution evaluated at each corresponding
value .
|
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
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
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
:Tensor
s structured liketype(model)
used to parameterize other dependent ("downstream") distribution-making functions. UsingNone
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
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 Tensor s 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 value
argument is also provided, raises a ValueError.
|
Returns | |
---|---|
distributions
|
a tuple of Distribution instances for each of
distribution_fn .
|
samples
|
a tuple of Tensor s with prepended dimensions sample_shape
for each of distribution_fn .
|
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
.
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
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 .
|
unnormalized_log_prob
unnormalized_log_prob(
*args, **kwargs
)
Unnormalized 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.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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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.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_prob
s---we could instead write
trivial_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
unnormalized_log_prob_parts(
*args, **kwargs
)
Unnormalized 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.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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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.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_parts
s---we could instead write
trivial_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 Tensor s
representing the unnormalized_log_prob for each component distribution
evaluated at each corresponding value .
|
unnormalized_prob_parts
unnormalized_prob_parts(
*args, **kwargs
)
Unnormalized 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.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)
JointDistribution
component distributions names are resolved via
jd._flat_resolve_names()
, which is implemented by each JointDistribution
subclass (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.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_parts
s---we could instead write
trivial_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 Tensor s
representing the unnormalized_prob for each component distribution
evaluated at each corresponding value .
|
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
.
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__
__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__
__iter__()