Joint distribution parameterized by a distribution-making generator.
Inherits From: JointDistribution, Distribution
oryx.distributions.JointDistributionCoroutine(
model,
sample_dtype=None,
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.
The JointDistributionCoroutine is specified by a generator that
generates the elements of this collection.
Mathematical Details
The JointDistributionCoroutine implements the chain rule of probability.
That is, the probability function of a length-d vector x is,
p(x) = prod{ p(x[i] | x[:i]) : i = 0, ..., (d - 1) }
The JointDistributionCoroutine is parameterized by a generator
that yields tfp.distributions.Distribution-like instances.
Each element yielded implements the i-th full conditional distribution,
p(x[i] | x[:i]). Within the generator, the return value from the yield
is a sample from the distribution that may be used to construct subsequent
yielded Distribution-like instances. This allows later instances
to be conditional on earlier ones.
Name resolution: The names of JointDistributionCoroutine components
may be specified by passing name arguments to distribution constructors (
`tfd.Normal(0., 1., name='x')). Components without an explicit name will be
assigned a dummy name.
Vectorized sampling and model evaluation
When a joint distribution's sample method is called with
a sample_shape (or the log_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 passing use_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 manually-vectorized joint distributions, each operation in the
model must account for the possibility of batch dimensions in Distributions
and their samples. By contrast, auto-vectorized 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
manually-vectorized 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 auto-vectorized 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.
Root annotations: When the sample method for a manually-vectorized
JointDistributionCoroutine is called with a sample_shape, the sample
method for each of the yielded distributions is called.
The distributions that have been wrapped in the
JointDistributionCoroutine.Root class will be called with sample_shape
as the sample_shape argument, and the unwrapped distributions
will be called with () as the sample_shape argument. It is the user's
responsibility to ensure that each of the distributions generates samples
with the specified sample size; generally this means applying Root wrappers
around any distributions whose parameters are not already a function of other
random variables. The Root annotation can be omitted if you never intend to
use a sample_shape other than ().
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
non-vectorized
while_loop. This limitation applies only in TensorFlow; vectorized samplers in JAX should be approximately as fast as manually vectorized code. - Calling
sample_distributionswith nontrivialsample_shapewill 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.Sampleis 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 'auto-batching' 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.
If batch_ndims==0, then the joint distribution has batch shape [], and all
component dimensions are treated as event shape. For example, the model
def model_fn():
x = yield tfd.Normal(0., tf.ones([3]))
y = yield tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2]))
jd = tfd.JointDistributionCoroutine(model_fn, batch_ndims=0)
creates a joint distribution with batch shape [] and event shape
([3], [3, 2]). The log-density of a sample always has shape
batch_shape, so this guarantees that
jd.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 setting batch_ndims=1, in which case
jd.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 backwards-compatibility reasons), in which the joint
distribution's log_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 with
tfd.Independent, as in this model:
def model_fn():
x = yield tfd.Normal(0., tf.ones([3]))
y = yield tfd.Independent(tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2])),
reinterpreted_batch_ndims=1)
jd = tfd.JointDistributionCoroutine(model_fn, batch_ndims=None)
Here the components both have batch shape [3], so
jd.log_prob(jd.sample()) returns a value of shape [3], just as in the
batch_ndims=1 case above. In fact, auto-batching semantics are equivalent to
implicitly wrapping each component dist as tfd.Independent(dist,
reinterpreted_batch_ndim=(dist.batch_shape.ndims - jd.batch_ndims)); the only
vestigial difference is that under auto-batching semantics, the joint
distribution has a single batch shape [3], while under the classic semantics
the value of jd.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.
Examples
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.JointDistributionCoroutine(model,
use_vectorized_map=True,
batch_ndims=0)
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 log-densities (because they are constructed with batch shape); the joint model implicitly sums over these to compute the single joint log-density.
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]]
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.JointDistributionCoroutine(model,
use_vectorized_map=True,
batch_ndims=0)
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.
References
[1] Dan Piponi, Dave Moore, and Joshua V. Dillon. Joint distributions for TensorFlow Probability. arXiv preprint arXiv:2001.11819_, 2020. https://arxiv.org/abs/2001.11819
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
@classmethodexperimental_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 Tensors, with prepended dimensions
sample_shape.
|
log_prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
|
is_scalar_batch
is_scalar_batch(
name='is_scalar_batch'
)
Indicates that batch_shape == [].
| 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_probs---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(
value, name='log_prob_parts'
)
Log probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors 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 Tensors 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
@classmethodparam_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
@classmethodparam_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
@classmethodparameter_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_shapeand_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 toParameterProperties`
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 probs---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(
value, name='prob_parts'
)
Probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors 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 Tensors 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.
Additional documentation from JointDistribution:
kwargs:
value:Tensors structured liketype(model)used to parameterize other dependent ("downstream") distribution-making functions. UsingNonefor 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 Tensors in distribution_fn order to use to
parameterize other ("downstream") distribution makers.
Default value: None (i.e., draw a sample from each distribution).
|
name
|
name prepended to ops created by this function.
Default value: "sample_distributions".
|
**kwargs
|
This is an alternative to passing a value, and achieves the
same effect. Named arguments will be used to parameterize other
dependent ("downstream") distribution-making functions. If a value
argument is also provided, raises a ValueError.
|
| Returns | |
|---|---|
distributions
|
a tuple of Distribution instances for each of
distribution_fn.
|
samples
|
a tuple of Tensors 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_probs---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(
value, name='unnormalized_log_prob_parts'
)
Unnormalized log probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors in distribution_fn order for which
we compute the unnormalized_log_prob_parts and to
parameterize other ("downstream") distributions.
|
name
|
name prepended to ops created by this function.
Default value: "unnormalized_log_prob_parts".
|
| Returns | |
|---|---|
unnormalized_log_prob_parts
|
a tuple of Tensors representing
the unnormalized_log_prob for each distribution_fn
evaluated at each corresponding value.
|
unnormalized_prob_parts
unnormalized_prob_parts(
value, name='unnormalized_prob_parts'
)
Unnormalized probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors in distribution_fn order for which
we compute the unnormalized_prob_parts and to parameterize
other ("downstream") distributions.
|
name
|
name prepended to ops created by this function.
Default value: "unnormalized_prob_parts".
|
| Returns | |
|---|---|
unnormalized_prob_parts
|
a tuple of Tensors representing the
unnormalized_prob for each distribution_fn 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__()