Joint distribution parameterized by distributionmaking functions.
Inherits From: JointDistribution
, Distribution
oryx.distributions.JointDistributionSequential(
model,
batch_ndims=None,
use_vectorized_map=False,
validate_args=False,
experimental_use_kahan_sum=False,
name=None
)
This distribution enables both sampling and joint probability computation from a single model specification.
A joint distribution is a collection of possibly interdependent distributions.
Like tf_keras.Sequential
, the JointDistributionSequential
can be specified
via a list
of functions (each responsible for making a
tfp.distributions.Distribution
like instance). Unlike
tf_keras.Sequential
, each function can depend on the output of all previous
elements rather than only the immediately previous.
#### Mathematical Details
The JointDistributionSequential
implements the chain rule of probability.
That is, the probability function of a lengthd
vector x
is,
p(x) = prod{ p(x[i]  x[:i]) : i = 0, ..., (d  1) }
The JointDistributionSequential
is parameterized by a list
comprised of
either:
tfp.distributions.Distribution
like instances or,callable
s which return atfp.distributions.Distribution
like instance.Each
list
element implements thei
th full conditional distribution,p(x[i]  x[:i])
. The "conditioned on" elements are represented by thecallable
's required arguments. Directly providing aDistribution
like instance is a convenience and is semantically identical a zero argumentcallable
.Denote the
i
thcallable
s nondefault arguments asargs[i]
. Since thecallable
is the conditional manifest,0 <= len(args[i]) <= i  1
. Whenlen(args[i]) < i  1
, thecallable
only depends on a subset of the previous distributions, specifically those at indexes:range(i  1, i  1  num_args[i], 1)
. (See "Examples" and "Discussion" for why the order is reversed.)Name resolution:
The names of
JointDistributionSequentialcomponents are defined by explicit
namearguments passed to distributions (
tfd.Normal(0., 1., name='x')) and/or by the argument names in distributionmaking functions (
lambda x: tfd.Normal(x., 1.)). Both approaches may be used in the same distribution, as long as they are consistent; referring to a single component by multiple names will raise a
ValueError`. Unnamed components will be assigned a dummy name.Examples
Consider the following generative model:
e ~ Exponential(rate=[100,120]) g ~ Gamma(concentration=e[0], rate=e[1]) n ~ Normal(loc=0, scale=2.) m ~ Normal(loc=n, scale=g) for i = 1, ..., 12: x[i] ~ Bernoulli(logits=m)
We can code this as:
tfd = tfp.distributions joint = tfd.JointDistributionSequential([ tfd.Exponential(rate=[100, 120]), # e lambda e: tfd.Gamma(concentration=e[0], rate=e[1]), # g tfd.Normal(loc=0, scale=2.), # n lambda n, g: tfd.Normal(loc=n, scale=g), # m lambda m: tfd.Sample(tfd.Bernoulli(logits=m), 12) # x ], batch_ndims=0, use_vectorized_map=True)
Notice the 1:1 correspondence between "math" and "code".
x = joint.sample() # ==> A length5 list of Tensors representing a draw/realization from each # distribution. joint.log_prob(x) # ==> A scalar `Tensor` representing the total log prob under all five # distributions. joint.resolve_graph() # ==> (('e', ()), # ('g', ('e',)), # ('n', ()), # ('m', ('n', 'g')), # ('x', ('m',)))
Discussion
JointDistributionSequential
builds each distribution inlist
order; list items must be either a:tfd.Distribution
like instance (e.g.,e
andn
), or aPython
callable
(e.g.,g
,m
,x
).Regarding #1, an object is deemed "
tfd.Distribution
like" if it has asample
,log_prob
, and distribution properties, e.g.,batch_shape
,event_shape
,dtype
.Regarding #2, in addition to using a function (or
lambda
), supplying a TFD "class
" is also permissible, this also being a "Pythoncallable
." For example, instead of writing:lambda loc, scale: tfd.Normal(loc=loc, scale=scale)
one could have simply writtentfd.Normal
.Notice that directly providing a
tfd.Distribution
like instance means there cannot exist a (dynamic) dependency on other distributions; it is "independent" both "computationally" and "statistically." The same is selfevidently true of zeroargumentcallable
s.A distribution instance depends on other distribution instances through the distribution making function's required arguments. If the distribution maker has
k
required arguments then theJointDistributionSequential
calls the maker with samples produced by the previousk
distributions.Vectorized sampling and model evaluation
When a joint distribution's
sample
method is called with asample_shape
(or thelog_prob
method is called on an input with multiple sample dimensions) the model must be equipped to handle additional batch dimensions. This may be done manually, or automatically by passinguse_vectorized_map=True
. Manual vectorization has historically been the default, but we now recommend that most users enable automatic vectorization unless they are affected by a specific issue; some known issues are listed below.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 as required using
tf.vectorized_map
(vmap
in JAX). In many cases this allows for significant simplications. For example, the following manuallyvectorizedtfd.JointDistributionSequential
model:model = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), tfd.Normal(0., 1.), lambda y, x: tfd.Normal(x[..., :2] + y[..., tf.newaxis], 1.) ])
can be written in autovectorized form as
model = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), tfd.Normal(0., 1.), lambda y, x: tfd.Normal(x[:2] + y, 1.) ], use_vectorized_map=True)
in which we were able to avoid explicitly accounting for batch dimensions when indexing and slicing computed quantities in the third line.
Known limitations of automatic vectorization:
 A small fraction of TensorFlow ops are unsupported; models that use an unsupported op will raise an error and must be manually vectorized.
 Sampling large batches may be slow under automatic vectorization because
TensorFlow's stateless samplers are currently converted using a
nonvectorized
while_loop
. This limitation applies only in TensorFlow; vectorized samplers in JAX should be approximately as fast as manually vectorized code. Calling
sample_distributions
with nontrivialsample_shape
will raise an error if the model contains any distributions that are not registered as CompositeTensors (TFP's basic distributions are usually fine, but support for wrapper distributions liketfd.Sample
is a work in progress).Batch semantics and (log)densities
tl;dr: pass
batch_ndims=0
unless you have a good reason not to.Joint distributions now support 'autobatching' semantics, in which the distribution's batch shape is derived by broadcasting the leftmost
batch_ndims
dimensions of its components' batch shapes. All remaining dimensions are considered to form a single 'event' of the joint distribution. Ifbatch_ndims==0
, then the joint distribution has batch shape[]
, and all component dimensions are treated as event shape. For example, the modeljd = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), lambda x: tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2])) ], batch_ndims=0)
creates a joint distribution with batch shape
[]
and event shape([3], [3, 2])
. The logdensity of a sample always has shapebatch_shape
, so this guarantees thatjd.log_prob(jd.sample())
will evaluate to a scalar value. We could alternately construct a joint distribution with batch shape[3]
and event shape([], [2])
by settingbatch_ndims=1
, in which casejd.log_prob(jd.sample())
would evaluate to a value of shape[3]
.Setting
batch_ndims=None
recovers the 'classic' batch semantics (currently still the default for backwardscompatibility reasons), in which the joint distribution'slog_prob
is computed by naively summing log densities from the component distributions. Since these component densities have shapes equal to the batch shapes of the individual components, to avoid broadcasting errors it is usually necessary to construct the components with identical batch shapes. For example, the component distributions in the model above have batch shapes of[3]
and[3, 2]
respectively, which would raise an error if summed directly, but can be aligned by wrapping withtfd.Independent
, as in this model:jd = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), lambda x: tfd.Independent(tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2])), reinterpreted_batch_ndims=1) ], batch_ndims=None)
Here the components both have batch shape
[3]
, sojd.log_prob(jd.sample())
returns a value of shape[3]
, just as in thebatch_ndims=1
case above. In fact, autobatching semantics are equivalent to implicitly wrapping each componentdist
astfd.Independent(dist, reinterpreted_batch_ndim=(dist.batch_shape.ndims  jd.batch_ndims))
; the only vestigial difference is that under autobatching semantics, the joint distribution has a single batch shape[3]
, while under the classic semantics the value ofjd.batch_shape
is a structure of the component batch shapes([3], [3])
. Such structured batch shapes will be deprecated in the future, since they are inconsistent with the definition of batch shapes used elsewhere in TFP.References
[1] Dan Piponi, Dave Moore, and Joshua V. Dillon. Joint distributions for TensorFlow Probability. arXiv preprint arXiv:2001.11819_,
If every element of model
is a CompositeTensor
or a callable, the resulting JointDistributionSequential
is a CompositeTensor
.Otherwise, a nonCompositeTensor
_JointDistributionSequential
instance is created.
Args  

model

Python list of either tfd.Distribution instances and/or
lambda functions which take the k previous distributions and returns a
new tfd.Distribution instance.

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: None .

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: False .

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 . This argument has no effect if
batch_ndims is None .
Default value: False .

name

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

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 1D Tensor
.
The batch dimensions are indexes into independent, nonidentical 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 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
.
other
types with builtin registrations: JointDistributionNamed
, JointDistributionNamedAutoBatched
, JointDistributionSequential
, JointDistributionSequentialAutoBatched
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.
Additional documentation from _JointDistributionSequential
:
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 1D 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 * (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_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 pushforward
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 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.
other
types with builtin registrations: JointDistributionNamed
, JointDistributionNamedAutoBatched
, JointDistributionSequential
, JointDistributionSequentialAutoBatched
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,
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.
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(
*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
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.
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
componentcreating a vectorshaped batch
of log_prob_parts
swe 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
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.
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 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.

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
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.
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(
*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
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.
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
componentcreating a vectorshaped batch
of prob_parts
swe 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 .

resolve_graph
resolve_graph(
distribution_names=None, leaf_name='x'
)
Creates a tuple
of tuple
s of dependencies.
This function is experimental. That said, we encourage its use
and ask that you report problems to tfprobability@tensorflow.org
.
Args  

distribution_names

list of str or None names corresponding to each
of model elements. (None s are expanding into the
appropriate str .)

leaf_name

str used when no maker depends on a particular
model element.

Returns  

graph

tuple of (str tuple) pairs representing the name of each
distribution (maker) and the names of its dependencies.

Example
d = tfd.JointDistributionSequential([
tfd.Independent(tfd.Exponential(rate=[100, 120]), 1),
lambda e: tfd.Gamma(concentration=e[..., 0], rate=e[..., 1]),
tfd.Normal(loc=0, scale=2.),
lambda n, g: tfd.Normal(loc=n, scale=g),
])
d.resolve_graph()
# ==> (
# ('e', ()),
# ('g', ('e',)),
# ('n', ()),
# ('x', ('n', 'g')),
# )
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") distributionmaking 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") distributionmaking 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

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 .

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
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.
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
componentcreating a vectorshaped batch
of unnormalized_log_prob
swe 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
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.
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
componentcreating a vectorshaped batch
of unnormalized_log_prob_parts
swe 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
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.
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
componentcreating a vectorshaped batch
of unnormalized_prob_parts
swe 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

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__()