Joint distribution parameterized by a distribution-making generator.
Inherits From: JointDistribution, Distribution
oryx.distributions.JointDistributionCoroutine(
model, sample_dtype=None, validate_args=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.
When the sample method for a 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.
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.
Examples
tfd = tfp.distributions
# 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)
# In TFP, we can write this as:
Root = tfd.JointDistributionCoroutine.Root # Convenient alias.
def model():
e = yield Root(tfd.Independent(tfd.Exponential(rate=[100, 120]), 1))
g = yield tfd.Gamma(concentration=e[..., 0], rate=e[..., 1])
n = yield Root(tfd.Normal(loc=0, scale=2.))
m = yield tfd.Normal(loc=n, scale=g)
joint = tfd.JointDistributionCoroutine(model)
x = joint.sample()
# ==> x is a length-4 tuple of Tensors representing a draw/realization from
# each distribution.
joint.log_prob(x)
# ==> A scalar `Tensor` representing the total log prob under all four
# distributions.
For improved readability of sampled values, the yielded distributions can also be named:
tfd = tfp.distributions
Root = tfd.JointDistributionCoroutine.Root # Convenient alias.
def model():
e = yield Root(tfd.Independent(
tfd.Exponential(rate=[100, 120]), 1), name='e')
g = yield tfd.Gamma(concentration=e[..., 0], rate=e[..., 1], name='g')
n = yield Root(tfd.Normal(loc=0, scale=2., name='n'))
m = yield tfd.Normal(loc=n, scale=g, name='m')
joint = tfd.JointDistributionCoroutine(model)
x = joint.sample()
# ==> x is a namedtuple with fields (in order) 'e', 'g', 'n', 'm' and values
# representing the draw/realization from each corresponding distribution.
joint.log_prob(x)
# ==> A scalar `Tensor` representing the total log prob under all four
# distributions.
# Passing dictionaries via `kwargs` also works.
joint.log_prob(**x._as_dict())
# Or:
joint.log_prob(e=..., g=..., n=..., m=...)
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.
Discussion
Each element yielded by the generator must be a tfd.Distribution-like
instance.
An object is deemed 'tfd.Distribution-like' if it has a
sample, log_prob, and distribution properties, e.g., batch_shape,
event_shape, dtype.
Consider the following fragment from a generator:
n = yield Root(tfd.Normal(loc=0, scale=2.))
m = yield tfd.Normal(loc=n, scale=1.0)
The random variable n has no dependence on earlier random variables and
Root is used to indicate that its distribution needs to be passed a
sample_shape. On the other hand, the distribution of m is constructed
using the value of n. This means that n is already shaped according to
the sample_shape and there is no need to pass m's distribution a
sample_size. So Root is not used to wrap m's distribution.
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(sampledtype, 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).
|
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.
|
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_shape
|
Shape of a single sample from a single event index as a TensorShape.
May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. |
dtype
|
The DType of Tensors handled by this Distribution.
|
event_shape
|
Shape of a single sample from a single batch as a TensorShape.
May be partially defined or unknown. |
experimental_shard_axis_names
|
Indicates whether part distributions have active shard axis names. |
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(
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_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.
| 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__()