|---|
| [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L246-L1158) |
Joint distribution over one or more component distributions.
Inherits From: [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution)
tfp.distributions.JointDistribution(
dtype,
validate_args,
parameters,
name,
use_vectorized_map=False,
batch_ndims=None,
experimental_use_kahan_sum=False
)
This distribution enables both sampling and joint probability computation from
a single model specification.
A joint distribution is a collection of possibly interdependent distributions.
> [!NOTE]
> **Note:** unlike other non-`JointDistribution` distributions in [`tfp.distributions`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions), [`JointDistribution.sample`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution#sample) (and subclasses) return a structure of `Tensor`s rather than a `Tensor`. A structure can be a `list`, `tuple`, `dict`, `collections.namedtuple`, etc. Accordingly `joint.batch_shape` returns a structure of `TensorShape`s for each of the distributions' batch shapes and `joint.batch_shape_tensor()` returns a structure of `Tensor`s for each of the distributions' event shapes. (Same with `event_shape` analogues.)
#### Subclass Requirements
#### Subclasses implement:
- `_model_coroutine`: A generator that yields a sequence of
`tfd.Distribution`-like instances.
- `_model_flatten`: takes a structured input and returns a sequence. The
sequence order must match the order distributions are yielded from
`_model_coroutine`.
- `_model_unflatten`: takes a sequence and returns a structure matching the
semantics of the `JointDistribution` subclass.
| ## Args ||
|---|---|
| `dtype` | The type of the event samples. `None` implies no type-enforcement. |
| `reparameterization_type` | Instance of `ReparameterizationType`. If `tfd.FULLY_REPARAMETERIZED`, then samples from the distribution are fully reparameterized, and straight-through gradients are supported. If `tfd.NOT_REPARAMETERIZED`, then samples from the distribution are not fully reparameterized, and straight-through gradients are either partially unsupported or are not supported at all. |
| `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. |
| `allow_nan_stats` | Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value "`NaN`" to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. |
| `parameters` | Python `dict` of parameters used to instantiate this `Distribution`. |
| `graph_parents` | Python `list` of graph prerequisites of this `Distribution`. |
| `name` | Python `str` name prefixed to Ops created by this class. Default: subclass name. |
| ## Raises ||
|---|---|
| `ValueError` | if any member of graph_parents is `None` or not a `Tensor`. |
| ## 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 `Tensor`s 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. |
| `name` | Name prepended to all ops created by this `Distribution`. |
| `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. |
| `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules.
> [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
| `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 `tfd.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.
> [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
| `use_vectorized_map` |
|
| `validate_args` | Python `bool` indicating possibly expensive checks are enabled. |
| `variables` | Sequence of variables owned by this module and its submodules.
> [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
## Child Classes
[`class Root`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution/Root)
## Methods
### `batch_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L992-L1030)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1411-L1429)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L896-L924)
copy(
**override_parameters_kwargs
)
Creates a deep copy of the distribution.
> [!NOTE]
> **Note:** the copy distribution may continue to depend on the original initialization arguments.
| 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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1648-L1686)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1701-L1724)
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`](https://www.tensorflow.org/probability/api_docs/python/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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1524-L1527)
entropy(
name='entropy', **kwargs
)
Shannon entropy in nats.
### `event_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1099-L1125)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1768-L1797)
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`](https://www.tensorflow.org/probability/api_docs/python/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()`](https://www.tensorflow.org/probability/api_docs/python/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`](https://www.tensorflow.org/probability/api_docs/python/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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1799-L1847)
@classmethod
experimental_fit(
value, sample_ndims=1, validate_args=False, **init_kwargs
)
Instantiates a distribution that maximizes the likelihood of `x`.
| Args ||
|---|---|
| `value` | a `Tensor` valid sample from this distribution family. |
| `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. |
| `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. |
| `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. |
| Returns ||
|---|---|
| `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. |
### `experimental_local_measure`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1872-L1914)
experimental_local_measure(
value, backward_compat=False, **kwargs
)
Returns a log probability density together with a `TangentSpace`.
A `TangentSpace` allows us to calculate the correct push-forward
density when we apply a transformation to a `Distribution` on
a strict submanifold of R\^n (typically via a `Bijector` in the
`TransformedDistribution` subclass). The density correction uses
the basis of the tangent space.
| Args ||
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R\^n with the standard basis. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns ||
|---|---|
| `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
| `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. |
| Raises ||
|---|---|
| UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. ||
### `experimental_pin`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L1112-L1158)
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`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/JointDistributionPinned) with the given values pinned. |
### `experimental_sample_and_log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1229-L1259)
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`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. |
| `name` | name to give to the op. Default value: `'sample_and_log_prob'`. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns ||
|---|---|
| `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. |
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `is_scalar_batch`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L660-L673)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L644-L658)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1730-L1761)
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`](https://www.tensorflow.org/probability/api_docs/python/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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1373-L1395)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L886-L899)
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_prob`s---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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L554-L576)
log_prob_parts(
*args, **kwargs
)
Log probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.log_prob_parts(sample) ==
jd.log_prob_parts(value=sample) ==
jd.log_prob_parts(z, x) ==
jd.log_prob_parts(z=z, x=x) ==
jd.log_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.log_prob_parts(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_parts`s---we could instead write
`trivial_jd.log_prob_parts(np.array([4]))`.
| Args ||
|---|---|
| `*args` | Positional arguments: a `value` structure or component values (see above). |
| `**kwargs` | Keyword arguments: a `value` structure or component values (see above). May also include `name`, specifying a Python string name for ops generated by this method. |
| Returns ||
|---|---|
| `log_prob_parts` | a `self.dtype`-like structure of `Tensor`s representing the `log_prob` for each component distribution evaluated at each corresponding `value`. |
### `log_survival_function`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1452-L1476)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1533-L1536)
mean(
name='mean', **kwargs
)
Mean.
### `mode`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1692-L1695)
mode(
name='mode', **kwargs
)
Mode.
### `param_shapes`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L701-L727)
@classmethod
param_shapes(
sample_shape, name='DistributionParamShapes'
)
Shapes of parameters given the desired shape of a call to `sample()`. (deprecated)
> [!WARNING]
> **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L729-L769)
@classmethod
param_static_shapes(
sample_shape
)
param_shapes with static (i.e. `TensorShape`) shapes. (deprecated)
> [!WARNING]
> **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_static_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L655-L699)
@classmethod
parameter_properties(
dtype=tf.float32, num_classes=None
)
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution's
`Tensor`-valued constructor arguments.
Distribution subclasses are not required to implement
`_parameter_properties`, so this method may raise `NotImplementedError`.
Providing a `_parameter_properties` implementation enables several advanced
features, including:
- Distribution batch slicing (`sliced_distribution = distribution[i:j]`).
- Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly.
- Automatic instantiation of the distribution within TFP's internal property tests.
- Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.
In the future, parameter property annotations may enable additional
functionality; for example, returning Distribution instances from
[`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/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.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. |
| Raises ||
|---|---|
| `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. |
### `prob`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L903-L916)
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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 `prob`s---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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L578-L597)
prob_parts(
*args, **kwargs
)
Probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.prob_parts(sample) ==
jd.prob_parts(value=sample) ==
jd.prob_parts(z, x) ==
jd.prob_parts(z=z, x=x) ==
jd.prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.prob_parts(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_parts`s---we could instead write
`trivial_jd.prob_parts(np.array([4]))`.
| Args ||
|---|---|
| `*args` | Positional arguments: a `value` structure or component values (see above). |
| `**kwargs` | Keyword arguments: a `value` structure or component values (see above). May also include `name`, specifying a Python string name for ops generated by this method. |
| Returns ||
|---|---|
| `prob_parts` | a `self.dtype`-like structure of `Tensor`s representing the `prob` for each component distribution evaluated at each corresponding `value`. |
### `quantile`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1555-L1573)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1189-L1205)
sample(
sample_shape=(), seed=None, name='sample', **kwargs
)
Generate samples of the specified shape.
Note that a call to `sample()` without arguments will generate a single
sample.
Additional documentation from `JointDistribution`:
##### `kwargs`:
- `value`: `Tensor`s structured 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).
| Args ||
|---|---|
| `sample_shape` | 0D or 1D `int32` `Tensor`. Shape of the generated samples. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L488-L542)
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`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. |
| `value` | `list` of `Tensor`s in `distribution_fn` order to use to parameterize other ("downstream") distribution makers. Default value: `None` (i.e., draw a sample from each distribution). |
| `name` | name prepended to ops created by this function. Default value: `"sample_distributions"`. |
| `**kwargs` | This is an alternative to passing a `value`, and achieves the same effect. Named arguments will be used to parameterize other dependent ("downstream") 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 `Tensor`s with prepended dimensions `sample_shape` for each of `distribution_fn`. |
### `stddev`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1613-L1642)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1498-L1518)
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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L920-L934)
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_prob`s---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`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L599-L621)
unnormalized_log_prob_parts(
*args, **kwargs
)
Unnormalized log probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_log_prob_parts(sample) ==
jd.unnormalized_log_prob_parts(value=sample) ==
jd.unnormalized_log_prob_parts(z, x) ==
jd.unnormalized_log_prob_parts(z=z, x=x) ==
jd.unnormalized_log_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_log_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_log_prob_parts(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_parts`s---we could instead write
`trivial_jd.unnormalized_log_prob_parts(np.array([4]))`.
| Args ||
|---|---|
| `*args` | Positional arguments: a `value` structure or component values (see above). |
| `**kwargs` | Keyword arguments: a `value` structure or component values (see above). May also include `name`, specifying a Python string name for ops generated by this method. |
| Returns ||
|---|---|
| `unnormalized_log_prob_parts` | a `self.dtype`-like structure of `Tensor`s representing the `unnormalized_log_prob` for each component distribution evaluated at each corresponding `value`. |
### `unnormalized_prob_parts`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution.py#L623-L642)
unnormalized_prob_parts(
*args, **kwargs
)
Unnormalized probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_prob_parts(sample) ==
jd.unnormalized_prob_parts(value=sample) ==
jd.unnormalized_prob_parts(z, x) ==
jd.unnormalized_prob_parts(z=z, x=x) ==
jd.unnormalized_prob_parts(z, x=x))
# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_prob_parts(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_prob_parts(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
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.
> [!NOTE]
> **Note:** not all `JointDistribution` subclasses support all calling styles; for example, `JointDistributionNamed` does not support positional arguments (aka "unnamed arguments") unless the provided model specifies an ordering of variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple` rather than a plain `dict`).
> [!NOTE]
> **Note:** care is taken to resolve any potential ambiguity---this is generally possible by inspecting the structure of the provided argument and "aligning" it to the joint distribution output structure (defined by `jd.dtype`). For example,
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_parts`s---we could instead write
`trivial_jd.unnormalized_prob_parts(np.array([4]))`.
| Args ||
|---|---|
| `*args` | Positional arguments: a `value` structure or component values (see above). |
| `**kwargs` | Keyword arguments: a `value` structure or component values (see above). May also include `name`, specifying a Python string name for ops generated by this method. |
| Returns ||
|---|---|
| `unnormalized_prob_parts` | a `self.dtype`-like structure of `Tensor`s representing the `unnormalized_prob` for each component distribution evaluated at each corresponding `value`. |
### `variance`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L1579-L1607)
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()`. |
### `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.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose
names included the module name:
mod = MyModule()
mod(tf.ones([1, 2]))
mod.w
| Args ||
|---|---|
| `method` | The method to wrap. |
| Returns ||
|---|---|
| The original method wrapped such that it enters the module's name scope. ||
### `__getitem__`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L825-L852)
__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__`
[View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/distribution.py#L854-L855)
__iter__()