Joint distribution parameterized by a distributionmaking generator.
Inherits From: JointDistributionCoroutine
, JointDistribution
, Distribution
oryx.distributions.JointDistributionCoroutineAutoBatched(
model, sample_dtype=None, batch_ndims=0, use_vectorized_map=True,
validate_args=False, experimental_use_kahan_sum=False, name=None
)
This class provides automatic vectorization and alternative semantics for
tfd.JointDistributionCoroutine
, which in many cases allows for
simplifications in the model specification.
Automatic vectorization
Autovectorized variants of JointDistribution allow the user to avoid
explicitly annotating a model's vectorization semantics.
When using manuallyvectorized joint distributions, each operation in the
model must account for the possibility of batch dimensions in Distributions
and their samples. By contrast, autovectorized models need only describe
a single sample from the joint distribution; any batch evaluation is
automated using tf.vectorized_map
as required. In many cases this
allows for significant simplications. For example, the following
manuallyvectorized tfd.JointDistributionCoroutine
model:
def model_fn():
x = yield tfd.JointDistributionCoroutine.Root(
tfd.Normal(0., tf.ones([3])))
y = yield tfd.JointDistributionCoroutine.Root(
tfd.Normal(0., 1.))
z = yield tfd.Normal(x[..., :2] + y[..., tf.newaxis], 1.)
can be written in autovectorized form as
```python
def model_fn():
x = yield tfd.Normal(0., tf.ones([3]))
y = yield tfd.Normal(0., 1.)
z = yield tfd.Normal(x[:2] + y, 1.)
in which we were able to drop the specification of Root
nodes and to
avoid explicitly accounting for batch dimensions when indexing and slicing
computed quantities in the third line.
Alternative batch semantics
This class also provides alternative semantics for specifying a batch of independent (nonidentical) joint distributions.
Instead of simply summing the log_prob
s of component distributions
(which may have different shapes), it first reduces the component log_prob
s
to ensure that jd.log_prob(jd.sample())
always returns a scalar, unless
batch_ndims
is explicitly set to a nonzero value (in which case the result
will have the corresponding tensor rank).
The essential changes are:
 An
event
ofJointDistributionCoroutineAutoBatched
is the list of tensors produced by.sample()
; thus, theevent_shape
is the list of the shapes of sampled tensors. These combine both the event and batch dimensions of the component distributions. By contrast, the event shape of a baseJointDistribution
s does not include batch dimensions of component distributions.  The
batch_shape
is a global property of the entire model, rather than a percomponent property as in baseJointDistribution
s. The global batch shape must be a prefix of the batch shapes of each component; the length of this prefix is specified by an optional argumentbatch_ndims
. Ifbatch_ndims
is not specified, the model has batch shape[]
.
Examples
A hierarchical model of Poisson logrates, written using
tfd.JointDistributionCoroutineAutoBatched
:
tfd = tfp.distributions
def model():
global_log_rate = yield tfd.Normal(loc=0., scale=1.)
local_log_rates = yield tfd.Normal(loc=0., scale=tf.ones([20]))
observed_counts = yield tfd.Poisson(
rate=tf.exp(global_log_rate + local_log_rates))
joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(joint.event_shape)
# ==> [[], [20], [20]]
print(joint.batch_shape)
# ==> []
xs = joint.sample()
print([x.shape for x in xs])
# ==> [[], [20], [20]]
lp = joint.log_prob(xs)
print(lp.shape)
# ==> []
Note that the component distributions of this model would, by themselves, return batches of logdensities (because they are constructed with batch shape); the joint model implicitly sums over these to compute the single joint logdensity.
ds, xs = joint.sample_distributions()
print([d.event_shape for d in ds])
# ==> [[], [], []] != model.event_shape
print([d.batch_shape for d in ds])
# ==> [[], [20], [20]] != model.batch_shape
print([d.log_prob(x).shape for (d, x) in zip(ds, xs)])
# ==> [[], [20], [20]]
The behavior of JointDistributionCoroutineAutoBatched
is (assuming that
batch_ndims
is not specified) equivalent to
adding tfp.distributions.Independent
wrappers to reinterpret all batch
dimensions in a JointDistributionCoroutine
model. That is, the model above
would be equivalently written using JointDistributionCoroutine
as:
def model_jdc():
global_log_rate = yield Root(tfd.Normal(0., 1.))
local_log_rates = yield Root(tfd.Independent(
tfd.Normal(0., tf.ones([20])), reinterpreted_batch_ndims=1))
observed_counts = yield Root(tfd.Independent(
tfd.Poisson(tf.exp(global_log_rate + local_log_rates)),
reinterpreted_batch_ndims=1))
joint_jdc = tfd.JointDistributionCoroutine(model_jdc)
To define a batch of joint distributions (independent, but not identical,
joint distributions from the same family) using
JointDistributionCoroutineAutoBatched
, any batch dimensions must be a shared
prefix of the batch dimensions for all components. The batch_ndims
argument
determines the size of the prefix to consider. For example, consider a simple
joint model with two scalar normal random variables, where the second
variable's mean is given by the first variable. We can write a batch of five
such models as:
def model():
x = yield tfd.Normal(0., scale=tf.ones([5]))
y = yield tfd.Normal(x, scale=[3., 2., 5., 1., 6.])
batch_joint = tfd.JointDistributionCoroutineAutoBatched(model, batch_ndims=1)
print(batch_joint.event_shape)
# ==> [[], []]
print(batch_joint.batch_shape)
# ==> [5]
print(batch_joint.log_prob(batch_joint.sample()).shape)
# ==> [5]
Note that if we had not passed batch_ndims
, this would be interpreted as a
single model over vectorvalued random variables (whose components happen to
be independent):
alternate_joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(alternate_joint.event_shape)
# ==> [[5], [5]]
print(alternate_joint.batch_shape)
# ==> []
print(alternate_joint.log_prob(batch_joint.sample()).shape)
# ==> []
For improved readability of sampled values, the yielded distributions can also be named:
tfd = tfp.distributions
def model():
global_log_rate = yield tfd.Normal(
loc=0., scale=1., name='global_log_rate')
local_log_rates = yield tfd.Normal(
loc=0., scale=tf.ones([20]), name='local_log_rates')
observed_counts = yield tfd.Poisson(
rate=tf.exp(global_log_rate + local_log_rates), name='observed_counts')
joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(joint.event_shape)
# ==> StructTuple(global_log_rate=[], local_log_rates=[20],
# observed_counts=[20])
print(joint.batch_shape)
# ==> []
xs = joint.sample()
print(['{}: {}'.format(k, x.shape) for k, x in xs._asdict().items()])
# ==> global_log_scale: []
# local_log_rates: [20]
# observed_counts: [20]
lp = joint.log_prob(xs)
print(lp.shape)
# ==> []
# Passing via `kwargs` also works.
lp = joint.log_prob(**xs._asdict())
# Or:
lp = joint.log_prob(
global_log_scale=...,
local_log_rates=...,
observed_counts=...,
)
If any of the yielded distributions are not explicitly named, they will
automatically be given a name of the form var#
where #
is the index of the
associated distribution. E.g. the first yielded distribution will have a
default name of var0
.
Args  

model

A generator that yields a sequence of tfd.Distribution like
instances.

sample_dtype

Samples from this distribution will be structured like
tf.nest.pack_sequence_as(sample_dtype, list_) . sample_dtype is only
used for tf.nest.pack_sequence_as structuring of outputs, never
casting (which is the responsibility of the component distributions).
Default value: None (i.e. namedtuple ).

batch_ndims

int Tensor number of batch dimensions. The batch_shape s
of all component distributions must be such that the prefixes of
length batch_ndims broadcast to a consistent joint batch shape.
Default value: 0 .

use_vectorized_map

Python bool . Whether to use tf.vectorized_map
to automatically vectorize evaluation of the model. This allows the
model specification to focus on drawing a single sample, which is often
simpler, but some ops may not be supported.
Default value: True .

validate_args

Python bool . Whether to validate input with asserts.
If validate_args is False , and the inputs are invalid,
correct behavior is not guaranteed.
Default value: False .

experimental_use_kahan_sum

Python bool . When True , we use Kahan
summation to aggregate independent underlying log_prob values, which
improves against the precision of a naive float32 sum. This can be
noticeable in particular for large dimensions in float32. See CPU caveat
on tfp.math.reduce_kahan_sum .

name

The name for ops managed by the distribution.
Default value: None (i.e., JointDistributionCoroutine ).

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


dtype

The DType of Tensor s handled by this Distribution .

event_shape


model


name

Name prepended to all ops created by this Distribution .

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 instances

trainable_variables


use_vectorized_map


validate_args

Python bool indicating possibly expensive checks are enabled.

variables

Child Classes
Methods
batch_shape_tensor
batch_shape_tensor(
sample_shape=(), name='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 nonscalarevent distributions.
For example, for a lengthk
, vectorvalued 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 nonvector, multivariate distributions (e.g.,
matrixvalued, 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
lengthk'
vector.
Args  

name

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

**kwargs

Named arguments forwarded to subclass implementation. 
Returns  

covariance

Floatingpoint 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(
sample_shape=(), name='event_shape_tensor'
)
Shape of a single sample from a single batch.
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 * (k1) // 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_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.

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 .

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 KullbackLeibler 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 KullbackLeibler
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,
```python
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
dictvalued JointDistribution, or implicitly, e.g., by the argument name of
a `JointDistributionSequential` distributionmaking functionthe provided
name will be used. Otherwise the component will receive a dummy name; these
may change without warning and should not be relied upon.
Note: not all `JointDistribution` subclasses support all calling styles;
for example, `JointDistributionNamed` does not support positional arguments
(aka "unnamed arguments") unless the provided model specifies an ordering of
variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple`
rather than a plain `dict`).
Note: care is taken to resolve any potential ambiguitythis is generally
possible by inspecting the structure of the provided argument and "aligning"
it to the joint distribution output structure (defined by `jd.dtype`). For
example,
```python
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` componentcreating a vectorshaped batch
of `log_prob`swe 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(
value, name='log_prob_parts'
)
Log probability density/mass function.
Args  

value

list of Tensor s in distribution_fn order for which we compute
the log_prob_parts and to parameterize other ("downstream")
distributions.

name

name prepended to ops created by this function.
Default value: "log_prob_parts" .

Returns  

log_prob_parts

a tuple of Tensor s representing the log_prob for
each distribution_fn 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
constantvalued 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.
Args  

dtype

Optional float dtype to assume for continuousvalued 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 categoricallike distributions.
Otherwise ignored.

Returns  

parameter_properties

A
str > tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names to ParameterProperties`
instances.

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,
```python
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
dictvalued JointDistribution, or implicitly, e.g., by the argument name of
a `JointDistributionSequential` distributionmaking functionthe provided
name will be used. Otherwise the component will receive a dummy name; these
may change without warning and should not be relied upon.
Note: not all `JointDistribution` subclasses support all calling styles;
for example, `JointDistributionNamed` does not support positional arguments
(aka "unnamed arguments") unless the provided model specifies an ordering of
variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple`
rather than a plain `dict`).
Note: care is taken to resolve any potential ambiguitythis is generally
possible by inspecting the structure of the provided argument and "aligning"
it to the joint distribution output structure (defined by `jd.dtype`). For
example,
```python
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` componentcreating a vectorshaped batch
of `prob`swe 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(
value, name='prob_parts'
)
Log probability density/mass function.
Args  

value

list of Tensor s in distribution_fn order for which we compute
the prob_parts and to parameterize other ("downstream") distributions.

name

name prepended to ops created by this function.
Default value: "prob_parts" .

Returns  

prob_parts

a tuple of Tensor s representing the prob for
each distribution_fn 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.
Args  

sample_shape

0D or 1D int32 Tensor . Shape of the generated samples.

seed

Python integer or tfp.util.SeedStream instance, for seeding PRNG.

name

name to give to the op. 
**kwargs

Named arguments forwarded to subclass implementation. 
Returns  

samples

a Tensor with prepended dimensions sample_shape .

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

Floatingpoint 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 .

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

Floatingpoint 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__()