tfp.distributions.JointDistributionCoroutineAutoBatched | TensorFlow Probability (original) (raw)
Joint distribution parameterized by a distribution-making generator.
Inherits From: JointDistributionCoroutine, JointDistribution, AutoCompositeTensorDistribution, Distribution, AutoCompositeTensor
tfp.distributions.JointDistributionCoroutineAutoBatched(
model,
sample_dtype=None,
batch_ndims=0,
use_vectorized_map=True,
validate_args=False,
experimental_use_kahan_sum=False,
name=None
)
Used in the notebooks
| Used in the tutorials |
|---|
| Probabilistic PCA Approximate inference for STS models with non-Gaussian observations |
This class provides automatic vectorization and alternative semantics fortfd.JointDistributionCoroutine, which in many cases allows for simplifications in the model specification.
Automatic vectorization
Auto-vectorized variants of JointDistribution allow the user to avoid explicitly annotating a model's vectorization semantics. 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 using tf.vectorized_map as required. 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.
Alternative batch semantics
This class also provides alternative semantics for specifying a batch of independent (non-identical) joint distributions.
Instead of simply summing the log_probs of component distributions (which may have different shapes), it first reduces the component log_probs to ensure that jd.log_prob(jd.sample()) always returns a scalar, unlessbatch_ndims is explicitly set to a nonzero value (in which case the result will have the corresponding tensor rank).
The essential changes are:
- An
eventofJointDistributionCoroutineAutoBatchedis the list of tensors produced by.sample(); thus, theevent_shapeis the list of the shapes of sampled tensors. These combine both the event and batch dimensions of the component distributions. By contrast, the event shape of a baseJointDistributions does not include batch dimensions of component distributions. - The
batch_shapeis a global property of the entire model, rather than a per-component property as in baseJointDistributions. The global batch shape must be a prefix of the batch shapes of each component; the length of this prefix is specified by an optional argumentbatch_ndims. Ifbatch_ndimsis not specified, the model has batch shape[].
Examples
A hierarchical model of Poisson log-rates, written usingtfd.JointDistributionCoroutineAutoBatched:
tfd = tfp.distributions
def model():
global_log_rate = yield tfd.Normal(loc=0., scale=1.)
local_log_rates = yield tfd.Normal(loc=0., scale=tf.ones([20]))
observed_counts = yield tfd.Poisson(
rate=tf.exp(global_log_rate + local_log_rates))
joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(joint.event_shape)
# ==> [[], [20], [20]]
print(joint.batch_shape)
# ==> []
xs = joint.sample()
print([x.shape for x in xs])
# ==> [[], [20], [20]]
lp = joint.log_prob(xs)
print(lp.shape)
# ==> []
Note that the component distributions of this model would, by themselves, return batches of 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]]
The behavior of JointDistributionCoroutineAutoBatched is (assuming thatbatch_ndims is not specified) equivalent to adding tfp.distributions.Independent wrappers to reinterpret all batch dimensions in a JointDistributionCoroutine model. That is, the model above would be equivalently written using JointDistributionCoroutine as:
def model_jdc():
global_log_rate = yield Root(tfd.Normal(0., 1.))
local_log_rates = yield Root(tfd.Independent(
tfd.Normal(0., tf.ones([20])), reinterpreted_batch_ndims=1))
observed_counts = yield Root(tfd.Independent(
tfd.Poisson(tf.exp(global_log_rate + local_log_rates)),
reinterpreted_batch_ndims=1))
joint_jdc = tfd.JointDistributionCoroutine(model_jdc)
To define a batch of joint distributions (independent, but not identical, joint distributions from the same family) usingJointDistributionCoroutineAutoBatched, any batch dimensions must be a shared prefix of the batch dimensions for all components. The batch_ndims argument determines the size of the prefix to consider. For example, consider a simple joint model with two scalar normal random variables, where the second variable's mean is given by the first variable. We can write a batch of five such models as:
def model():
x = yield tfd.Normal(0., scale=tf.ones([5]))
y = yield tfd.Normal(x, scale=[3., 2., 5., 1., 6.])
batch_joint = tfd.JointDistributionCoroutineAutoBatched(model, batch_ndims=1)
print(batch_joint.event_shape)
# ==> [[], []]
print(batch_joint.batch_shape)
# ==> [5]
print(batch_joint.log_prob(batch_joint.sample()).shape)
# ==> [5]
Note that if we had not passed batch_ndims, this would be interpreted as a single model over vector-valued random variables (whose components happen to be independent):
alternate_joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(alternate_joint.event_shape)
# ==> [[5], [5]]
print(alternate_joint.batch_shape)
# ==> []
print(alternate_joint.log_prob(batch_joint.sample()).shape)
# ==> []
For improved readability of sampled values, the yielded distributions can also be named:
tfd = tfp.distributions
def model():
global_log_rate = yield tfd.Normal(
loc=0., scale=1., name='global_log_rate')
local_log_rates = yield tfd.Normal(
loc=0., scale=tf.ones([20]), name='local_log_rates')
observed_counts = yield tfd.Poisson(
rate=tf.exp(global_log_rate + local_log_rates), name='observed_counts')
joint = tfd.JointDistributionCoroutineAutoBatched(model)
print(joint.event_shape)
# ==> StructTuple(global_log_rate=[], local_log_rates=[20],
# observed_counts=[20])
print(joint.batch_shape)
# ==> []
xs = joint.sample()
print(['{}: {}'.format(k, x.shape) for k, x in xs._asdict().items()])
# ==> global_log_scale: []
# local_log_rates: [20]
# observed_counts: [20]
lp = joint.log_prob(xs)
print(lp.shape)
# ==> []
# Passing via `kwargs` also works.
lp = joint.log_prob(**xs._asdict())
# Or:
lp = joint.log_prob(
global_log_scale=...,
local_log_rates=...,
observed_counts=...,
)
If any of the yielded distributions are not explicitly named, they will automatically be given a name of the form var# where # is the index of the associated distribution. E.g. the first yielded distribution will have a default name of var0.
| Args | |
|---|---|
| model | A generator that yields a sequence of tfd.Distribution-like instances. |
| sample_dtype | Samples from this distribution will be structured liketf.nest.pack_sequence_as(sample_dtype, list_). sample_dtype is only used for tf.nest.pack_sequence_as structuring of outputs, never casting (which is the responsibility of the component distributions). Default value: None (i.e. namedtuple). |
| batch_ndims | int Tensor number of batch dimensions. The batch_shapes of all component distributions must be such that the prefixes of length batch_ndims broadcast to a consistent joint batch shape. Default value: 0. |
| use_vectorized_map | Python bool. Whether to use tf.vectorized_mapto automatically vectorize evaluation of the model. This allows the model specification to focus on drawing a single sample, which is often simpler, but some ops may not be supported. Default value: True. |
| validate_args | Python bool. Whether to validate input with asserts. If validate_args is False, and the inputs are invalid, correct behavior is not guaranteed. Default value: False. |
| experimental_use_kahan_sum | Python bool. When True, we use Kahan summation to aggregate independent underlying log_prob values, which improves against the precision of a naive float32 sum. This can be noticeable in particular for large dimensions in float32. See CPU caveat on tfp.math.reduce_kahan_sum. |
| name | The name for ops managed by the distribution. Default value: None (i.e., JointDistributionCoroutine). |
| Attributes | |
|---|---|
| allow_nan_stats | Python bool describing behavior when a stat is undefined.Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined. |
| batch_ndims | |
| batch_shape | 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. |
| name_scope | Returns a tf.name_scope instance for this class. |
| non_trainable_variables | Sequence of non-trainable variables owned by this module and its submodules. |
| 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 instancestfd.FULLY_REPARAMETERIZED or tfd.NOT_REPARAMETERIZED. |
| submodules | Sequence of all sub-modules.Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). a = tf.Module() b = tf.Module() c = tf.Module() a.b = b b.c = c list(a.submodules) == [b, c] True list(b.submodules) == [c] True list(c.submodules) == [] True |
| trainable_variables | Sequence of trainable variables owned by this module and its submodules. |
| use_vectorized_map | |
| validate_args | Python bool indicating possibly expensive checks are enabled. |
| variables | Sequence of variables owned by this module and its submodules. |
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 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.
| 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 andk' = 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 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.
| 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 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.
| Args | |
|---|---|
| *args | Passed to implementation _default_event_space_bijector. |
| **kwargs | Passed to implementation _default_event_space_bijector. |
| Returns | |
|---|---|
| event_space_bijector | Bijector instance or None. |
experimental_fit
@classmethod
experimental_fit( value, sample_ndims=1, validate_args=False, **init_kwargs )
Instantiates a distribution that maximizes the likelihood of x.
| Args | |
|---|---|
| value | a Tensor valid sample from this distribution family. |
| sample_ndims | Positive int Tensor number of leftmost dimensions ofvalue 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 tocls.__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 theTransformedDistribution 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 returningFullSpace 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 shapesample_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'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)
| 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 dimensionssample_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 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.
| 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 whenx << -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 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| log_prob | a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype. |
log_prob_parts
log_prob_parts(
*args, **kwargs
)
Log probability density/mass function.
The measure methods of JointDistribution (log_prob, prob, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.log_prob_parts(sample) ==
jd.log_prob_parts(value=sample) ==
jd.log_prob_parts(z, x) ==
jd.log_prob_parts(z=z, x=x) ==
jd.log_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.log_prob_parts(**sample)
JointDistribution component distributions names are resolved 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| log_prob_parts | a self.dtype-like structure of Tensors representing the log_prob for each component distribution evaluated at each corresponding value. |
log_survival_function
log_survival_function(
value, name='log_survival_function', **kwargs
)
Log survival function.
Given random variable X, the survival function is defined:
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.
| Args | |
|---|---|
| value | float or double Tensor. |
| name | Python str prepended to names of ops created by this function. |
| **kwargs | Named arguments forwarded to subclass implementation. |
| Returns |
|---|
| Tensor of shape sample_shape(x) + self.batch_shape with values of typeself.dtype. |
mean
mean(
name='mean', **kwargs
)
Mean.
mode
mode(
name='mode', **kwargs
)
Mode.
param_shapes
@classmethod
param_shapes( sample_shape, name='DistributionParamShapes' )
Shapes of parameters given the desired shape of a call to sample(). (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.
| Args | |
|---|---|
| sample_shape | Tensor or python list/tuple. Desired shape of a call tosample(). |
| name | name to prepend ops with. |
| Returns |
|---|
| dict of parameter name to Tensor shapes. |
param_static_shapes
@classmethod
param_static_shapes( sample_shape )
param_shapes with static (i.e. TensorShape) shapes. (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.
| Args | |
|---|---|
| sample_shape | TensorShape or python list/tuple. Desired shape of a call to sample(). |
| Returns |
|---|
| dict of parameter name to TensorShape. |
| Raises | |
|---|---|
| ValueError | if sample_shape is a TensorShape and is not fully defined. |
parameter_properties
@classmethod
parameter_properties( dtype=tf.float32, num_classes=None )
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution'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_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 fromtf.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 | Astr ->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 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| prob | a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype. |
prob_parts
prob_parts(
*args, **kwargs
)
Probability density/mass function.
The measure methods of JointDistribution (log_prob, prob, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.prob_parts(sample) ==
jd.prob_parts(value=sample) ==
jd.prob_parts(z, x) ==
jd.prob_parts(z=z, x=x) ==
jd.prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.prob_parts(**sample)
JointDistribution component distributions names are resolved 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| prob_parts | a self.dtype-like structure of Tensors representing theprob for each component distribution evaluated at each correspondingvalue. |
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 valueargument is also provided, raises a ValueError. |
| Returns | |
|---|---|
| distributions | a tuple of Distribution instances for each ofdistribution_fn. |
| samples | a tuple of Tensors with prepended dimensions sample_shapefor 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, Edenotes 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 tobatch_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 typeself.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 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| log_prob | a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype. |
unnormalized_log_prob_parts
unnormalized_log_prob_parts(
*args, **kwargs
)
Unnormalized log probability density/mass function.
The measure methods of JointDistribution (log_prob, prob, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_log_prob_parts(sample) ==
jd.unnormalized_log_prob_parts(value=sample) ==
jd.unnormalized_log_prob_parts(z, x) ==
jd.unnormalized_log_prob_parts(z=z, x=x) ==
jd.unnormalized_log_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_log_prob_parts(**sample)
JointDistribution component distributions names are resolved 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| unnormalized_log_prob_parts | a self.dtype-like structure of Tensors representing the unnormalized_log_prob for each component distribution evaluated at each corresponding value. |
unnormalized_prob_parts
unnormalized_prob_parts(
*args, **kwargs
)
Unnormalized probability density/mass function.
The measure methods of JointDistribution (log_prob, prob, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_prob_parts(sample) ==
jd.unnormalized_prob_parts(value=sample) ==
jd.unnormalized_prob_parts(z, x) ==
jd.unnormalized_prob_parts(z=z, x=x) ==
jd.unnormalized_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_prob_parts(**sample)
JointDistribution component distributions names are resolved 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])).
| Args | |
|---|---|
| *args | Positional arguments: a value structure or component values (see above). |
| **kwargs | Keyword arguments: a value structure or component values (see above). May also include name, specifying a Python string name for ops generated by this method. |
| Returns | |
|---|---|
| unnormalized_prob_parts | a self.dtype-like structure of Tensors representing the unnormalized_prob for each component distribution evaluated at each corresponding value. |
variance
variance(
name='variance', **kwargs
)
Variance.
Variance is defined as,
Var = E[(X - E[X])**2]
where X is the random variable associated with this distribution, Edenotes 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 tobatch_shape + event_shape, i.e., the same shape as self.mean(). |
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)>
| Args | |
|---|---|
| method | The method to wrap. |
| Returns |
|---|
| The original method wrapped such that it enters the module's name scope. |
__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.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]
| Args | |
|---|---|
| slices | slices from the [] operator |
| Returns | |
|---|---|
| dist | A new tfd.Distribution instance with sliced parameters. |
__iter__
__iter__()