tfp.distributions.JointDistributionSequential  |  TensorFlow Probability (original) (raw)

Joint distribution parameterized by distribution-making functions.

Inherits From: JointDistribution, Distribution

tfp.distributions.JointDistributionSequential(
    model,
    batch_ndims=None,
    use_vectorized_map=False,
    validate_args=False,
    experimental_use_kahan_sum=False,
    name=None
)

Used in the notebooks

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 atfp.distributions.Distribution-like instance). Unliketf.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 length-d 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:

1. tfp.distributions.Distribution-like instances or,
2. callables which return a tfp.distributions.Distribution-like instance.
   Each list element implements the i-th full conditional distribution,p(x[i] | x[:i]). The "conditioned on" elements are represented by thecallable's required arguments. Directly providing a Distribution-like instance is a convenience and is semantically identical a zero argumentcallable.
   Denote the i-th callables non-default arguments as args[i]. Since thecallable is the conditional manifest, 0 <= len(args[i]) <= i - 1. Whenlen(args[i]) < i - 1, the callable 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 ofJointDistributionSequentialcomponents are defined by explicitnamearguments passed to distributions (tfd.Normal(0., 1., name='x')) and/or by the argument names in distribution-making 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 aValueError`. 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 length-5 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 in list order; list items must be either a: 3. tfd.Distribution-like instance (e.g., e and n), or a 4. Python 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 "Python callable." For example, instead of writing:lambda loc, scale: tfd.Normal(loc=loc, scale=scale)one could have simply written tfd.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 self-evidently true of zero-argument callables.
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 the JointDistributionSequential calls the maker with samples produced by the previous k distributions.

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.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 auto-vectorized 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 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_distributions with nontrivial sample_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 like tfd.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 'auto-batching' semantics, in which the distribution's batch shape is derived by broadcasting the leftmostbatch_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

jd = 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 log-density 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 setting batch_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 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 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, 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.

References

[1] Dan Piponi, Dave Moore, and Joshua V. Dillon. Joint distributions for TensorFlow Probability. arXiv preprint arXiv:2001.11819_,

1. https://arxiv.org/abs/2001.11819

If every element of model is a CompositeTensor or a callable, the resulting JointDistributionSequential is a CompositeTensor.Otherwise, a non-CompositeTensor _JointDistributionSequential instance is created.

Child Classes

class Root

Methods

batch_shape_tensor

View source

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.

cdf

View source

cdf(
    value, name='cdf', **kwargs
)

Cumulative distribution function.

Given random variable X, the cumulative distribution function cdf is:

cdf(x) := P[X <= x]

copy

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copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

covariance

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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 Edenotes 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.

cross_entropy

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cross_entropy(
    other, name='cross_entropy'
)

Computes the (Shannon) cross entropy.

Denote this distribution (self) by P and the other distribution byQ. 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 built-in registrations: JointDistributionNamed, JointDistributionNamedAutoBatched, JointDistributionSequential, JointDistributionSequentialAutoBatched

entropy

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entropy(
    name='entropy', **kwargs
)

Shannon entropy in nats.

Additional documentation from _JointDistributionSequential:

Shannon entropy in nats.

event_shape_tensor

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event_shape_tensor(
    name='event_shape_tensor'
)

Shape of a single sample from a single batch as a 1-D int32 Tensor.

experimental_default_event_space_bijector

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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 oftfp.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 theCholeskyLKJ 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.

experimental_fit

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@classmethod experimental_fit( value, sample_ndims=1, validate_args=False, **init_kwargs )

Instantiates a distribution that maximizes the likelihood of x.

experimental_local_measure

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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 theTransformedDistribution subclass). The density correction uses the basis of the tangent space.

experimental_pin

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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'svalue 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)

experimental_sample_and_log_prob

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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.

is_scalar_batch

View source

is_scalar_batch(
    name='is_scalar_batch'
)

Indicates that batch_shape == [].

is_scalar_event

View source

is_scalar_event(
    name='is_scalar_event'
)

Indicates that event_shape == [].

kl_divergence

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kl_divergence(
    other, name='kl_divergence'
)

Computes the Kullback--Leibler divergence.

Denote this distribution (self) by p and the other distribution byq. 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 built-in registrations: JointDistributionNamed, JointDistributionNamedAutoBatched, JointDistributionSequential, JointDistributionSequentialAutoBatched

log_cdf

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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 whenx << -1.

log_prob

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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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (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 writetrivial_jd.log_prob(np.array([4])).

log_prob_parts

View source

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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (see subclass documentation for details). Generally, for components where a name was provided--- either explicitly as the name argument to a distribution or as a key in a dict-valued JointDistribution, or implicitly, e.g., by the argument name of a JointDistributionSequential distribution-making function---the provided name will be used. Otherwise the component will receive a dummy name; these may change without warning and should not be relied upon.

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.log_prob_parts([4.])
# ==> Tensor with shape `[]`.
lp_parts = trivial_jd.log_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of log_prob_partss---we could instead writetrivial_jd.log_prob_parts(np.array([4])).

log_survival_function

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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.

mean

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mean(
    name='mean', **kwargs
)

Mean.

mode

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mode(
    name='mode', **kwargs
)

Mode.

param_shapes

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@classmethod param_shapes( sample_shape, name='DistributionParamShapes' )

Shapes of parameters given the desired shape of a call to sample(). (deprecated)

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.

param_static_shapes

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@classmethod param_static_shapes( sample_shape )

param_shapes with static (i.e. TensorShape) shapes. (deprecated)

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.

parameter_properties

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@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'sTensor-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 fromtf.vectorized_map.

prob

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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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (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 writetrivial_jd.prob(np.array([4])).

prob_parts

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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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (see subclass documentation for details). Generally, for components where a name was provided--- either explicitly as the name argument to a distribution or as a key in a dict-valued JointDistribution, or implicitly, e.g., by the argument name of a JointDistributionSequential distribution-making function---the provided name will be used. Otherwise the component will receive a dummy name; these may change without warning and should not be relied upon.

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.prob_parts([4.])
# ==> Tensor with shape `[]`.
p_parts = trivial_jd.prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of prob_partss---we could instead writetrivial_jd.prob_parts(np.array([4])).

quantile

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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

resolve_graph

View source

resolve_graph(
    distribution_names=None, leaf_name='x'
)

Creates a tuple of tuples of dependencies.

This function is experimental. That said, we encourage its use and ask that you report problems to tfprobability@tensorflow.org.

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

View source

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 like type(model) used to parameterize other dependent ("downstream") distribution-making functions. Using None for any element will trigger a sample from the corresponding distribution. Default value: None (i.e., draw a sample from each distribution).

sample_distributions

View source

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.

stddev

View source

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, Edenotes expectation, and stddev.shape = batch_shape + event_shape.

survival_function

View source

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).

unnormalized_log_prob

View source

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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (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 writetrivial_jd.unnormalized_log_prob(np.array([4])).

unnormalized_log_prob_parts

View source

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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (see subclass documentation for details). Generally, for components where a name was provided--- either explicitly as the name argument to a distribution or as a key in a dict-valued JointDistribution, or implicitly, e.g., by the argument name of a JointDistributionSequential distribution-making function---the provided name will be used. Otherwise the component will receive a dummy name; these may change without warning and should not be relied upon.

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.unnormalized_log_prob_parts([4.])
# ==> Tensor with shape `[]`.
unnorm_lp_parts = trivial_jd.unnormalized_log_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of unnormalized_log_prob_partss---we could instead writetrivial_jd.unnormalized_log_prob_parts(np.array([4])).

unnormalized_prob_parts

View source

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 viajd._flat_resolve_names(), which is implemented by each JointDistributionsubclass (see subclass documentation for details). Generally, for components where a name was provided--- either explicitly as the name argument to a distribution or as a key in a dict-valued JointDistribution, or implicitly, e.g., by the argument name of a JointDistributionSequential distribution-making function---the provided name will be used. Otherwise the component will receive a dummy name; these may change without warning and should not be relied upon.

trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)])
trivial_jd.dtype  # => [tf.float32]
trivial_jd.unnormalized_prob_parts([4.])
# ==> Tensor with shape `[]`.
unnorm_prob_parts = trivial_jd.unnormalized_prob_parts(4.)
# ==> Tensor with shape `[]`.

Notice that in the first call, [4.] is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the Exponential component---creating a vector-shaped batch of unnormalized_prob_partss---we could instead writetrivial_jd.unnormalized_prob_parts(np.array([4])).

variance

View source

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, Edenotes expectation, and Var.shape = batch_shape + event_shape.

with_name_scope

@classmethod with_name_scope( method )

Decorator to automatically enter the module name scope.

class MyModule(tf.Module): @tf.Module.with_name_scope def __call__(self, x): if not hasattr(self, 'w'): self.w = tf.Variable(tf.random.normal([x.shape[1], 3])) return tf.matmul(x, self.w)

Using the above module would produce tf.Variables and tf.Tensors whose names included the module name:

mod = MyModule() mod(tf.ones([1, 2])) <tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)> mod.w <tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32, numpy=..., dtype=float32)>

__getitem__

View source

__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.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.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]

__iter__

View source

__iter__()