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# tfp.distributions.JointDistributionSequentialAutoBatched

Joint distribution parameterized by distribution-making functions.

This class provides automatic vectorization and alternative semantics for `tfd.JointDistributionNamed`, 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.JointDistributionSequential` model:

``````model = tfd.JointDistributionSequential([
tfd.Normal(0., tf.ones([3])),
tfd.Normal(0., 1.),
lambda y, x: tfd.Normal(x[..., :2] + y[..., tf.newaxis], 1.)
])
``````

can be written in auto-vectorized form as

``````model = tfd.JointDistributionAutoBatchedSequential([
tfd.Normal(0., tf.ones([3])),
tfd.Normal(0., 1.),
lambda y, x: tfd.Normal(x[:2] + y, 1.)
])
``````

in which we were able 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_prob`s of component distributions (which may have different shapes), it first reduces the component `log_prob`s to ensure that `jd.log_prob(jd.sample())` always returns a scalar, unless `batch_ndims` is explicitly set to a nonzero value (in which case the result will have the corresponding tensor rank).

The essential changes are:

• An `event` of `JointDistributionSequentialAutoBatched` is the list of tensors produced by `.sample()`; thus, the `event_shape` is the list containing the shapes of sampled tensors. These combine both the event and batch dimensions of the component distributions. By contrast, the event shape of a base `JointDistribution`s does not include batch dimensions of component distributions.
• The `batch_shape` is a global property of the entire model, rather than a per-component property as in base `JointDistribution`s. 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 argument `batch_ndims`. If `batch_ndims` is not specified, the model has batch shape `[]`.

#### Examples

Consider the following generative model:

``````e ~ Exponential(rate=[100,120])
g ~ Gamma(concentration=e[0], rate=e[1])
n ~ Normal(loc=0, scale=2.)
m ~ Normal(loc=n, scale=g)
for i = 1, ..., 12:
x[i] ~ Bernoulli(logits=m)
``````

#### We can code this as:

``````tfd = tfp.distributions
joint = tfd.JointDistributionSequentialAutoBatched([
tfd.Exponential(rate=[100, 120]), 1,         # e
lambda    e: tfd.Gamma(concentration=e[0], rate=e[1]),    # g
tfd.Normal(loc=0, scale=2.),                 # n
lambda n, g: tfd.Normal(loc=n, scale=g)                   # m
lambda    m: tfd.Sample(tfd.Bernoulli(logits=m), 12)      # x
])
``````

Notice the 1:1 correspondence between "math" and "code". In a standard `JointDistributionSequential`, we would have wrapped the first variable as ```e = tfd.Independent(tfd.Exponential(rate=[100, 120]), reinterpreted_batch_ndims=1)``` to specify that `log_prob` of the `Exponential` should be a scalar, summing over both dimensions. We would also have had to extend indices as `tfd.Gamma(concentration=e[..., 0], rate=e[..., 1])` to account for possible batch dimensions. Both of these behaviors are implicit in `JointDistributionSequentialAutoBatched`.

`model` A generator that yields a sequence of `tfd.Distribution`-like instances.
`batch_ndims` `int` `Tensor` number of batch dimensions. The `batch_shape`s 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_map` to 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., `JointDistributionSequential`).

`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.
`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 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.

`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

`class Root`

## Methods

### `batch_shape_tensor`

View source

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

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

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`

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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`

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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`.

`other` types with built-in registrations: `JointDistributionNamed`, `JointDistributionNamedAutoBatched`, `JointDistributionSequential`, `JointDistributionSequentialAutoBatched`

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`

View source

Shannon entropy in nats.

Additional documentation from `JointDistributionSequential`:

Shannon entropy in nats.

### `event_shape_tensor`

View source

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

Bijector mapping the reals (R**n) to the event space of the distribution.

Distributions with continuous support may implement `_default_event_space_bijector` which returns a subclass of `tfp.bijectors.Bijector` that maps R**n to the distribution's event space. For example, the default bijector for the `Beta` distribution is `tfp.bijectors.Sigmoid()`, which maps the real line to `[0, 1]`, the support of the `Beta` distribution. The default bijector for the `CholeskyLKJ` distribution is `tfp.bijectors.CorrelationCholesky`, which maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal.

The purpose of `experimental_default_event_space_bijector` is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential.

For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns `None`.

Args
`*args` Passed to implementation `_default_event_space_bijector`.
`**kwargs` Passed to implementation `_default_event_space_bijector`.

Returns
`event_space_bijector` `Bijector` instance or `None`.

### `experimental_fit`

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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`

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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`

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Pins some parts, returning an unnormalized distribution object.

The calling convention is much like other `JointDistribution` methods (e.g. `log_prob`), but with the difference that not all parts are required. In this respect, the behavior is similar to that of the `sample` function's `value` argument.

### Examples:

``````# Given the following joint distribution:
jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1., name='z'),
tfd.Normal(0., 1., name='y'),
lambda y, z: tfd.Normal(y + z, 1., name='x')
], validate_args=True)

# The following calls are all permissible and produce
# `JointDistributionPinned` objects behaving identically.
PartialXY = collections.namedtuple('PartialXY', 'x,y')
PartialX = collections.namedtuple('PartialX', 'x')
assert (jd.experimental_pin(x=2.).pins ==
jd.experimental_pin(x=2., z=None).pins ==
jd.experimental_pin(dict(x=2.)).pins ==
jd.experimental_pin(dict(x=2., y=None)).pins ==
jd.experimental_pin(PartialXY(x=2., y=None)).pins ==
jd.experimental_pin(PartialX(x=2.)).pins ==
jd.experimental_pin(None, None, 2.).pins ==
jd.experimental_pin([None, None, 2.]).pins)
``````

Args
`*args` Positional arguments: a value structure or component values (see above).
`**kwargs` Keyword arguments: a value structure or component values (see above). May also include `name`, specifying a Python string name for ops generated by this method.

Returns
`pinned` a `tfp.experimental.distributions.JointDistributionPinned` with the given values pinned.

### `experimental_sample_and_log_prob`

View source

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 `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

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`

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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

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.

`other` types with built-in registrations: `JointDistributionNamed`, `JointDistributionNamedAutoBatched`, `JointDistributionSequential`, `JointDistributionSequentialAutoBatched`

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`

View source

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

Log probability density/mass function.

The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,

``````jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.log_prob(sample) ==
jd.log_prob(value=sample) ==
jd.log_prob(z, x) ==
jd.log_prob(z=z, x=x) ==
jd.log_prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.log_prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.log_prob(**sample)
``````

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

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

Notice that in the first call, `[4.]` is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the `Exponential` component---creating a vector-shaped batch of `log_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

Log probability density/mass function.

Args
`value` `list` of `Tensor`s in `distribution_fn` order for which we compute the `log_prob_parts` and to parameterize other ("downstream") distributions.
`name` name prepended to ops created by this function. Default value: `"log_prob_parts"`.

Returns
`log_prob_parts` a `tuple` of `Tensor`s representing the `log_prob` for each `distribution_fn` evaluated at each corresponding `value`.

### `log_survival_function`

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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`.

View source

Mean.

View source

Mode.

### `param_shapes`

View source

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 to `sample()`.
`name` name to prepend ops with.

Returns
`dict` of parameter name to `Tensor` shapes.

### `param_static_shapes`

View source

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`

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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`.

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

Probability density/mass function.

The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,

``````jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.prob(sample) ==
jd.prob(value=sample) ==
jd.prob(z, x) ==
jd.prob(z=z, x=x) ==
jd.prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.prob(**sample)
``````

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

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

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

Probability density/mass function.

Args
`value` `list` of `Tensor`s in `distribution_fn` order for which we compute the `prob_parts` and to parameterize other ("downstream") distributions.
`name` name prepended to ops created by this function. Default value: `"prob_parts"`.

Returns
`prob_parts` a `tuple` of `Tensor`s representing the `prob` for each `distribution_fn` evaluated at each corresponding `value`.

### `quantile`

View source

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`.

### `resolve_graph`

View source

Creates a `tuple` of `tuple`s of dependencies.

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

Args
`distribution_names` `list` of `str` or `None` names corresponding to each of `model` elements. (`None`s are expanding into the appropriate `str`.)
`leaf_name` `str` used when no maker depends on a particular `model` element.

Returns
`graph` `tuple` of `(str tuple)` pairs representing the name of each distribution (maker) and the names of its dependencies.

#### Example

``````d = tfd.JointDistributionSequential([
tfd.Independent(tfd.Exponential(rate=[100, 120]), 1),
lambda    e: tfd.Gamma(concentration=e[..., 0], rate=e[..., 1]),
tfd.Normal(loc=0, scale=2.),
lambda n, g: tfd.Normal(loc=n, scale=g),
])
d.resolve_graph()
# ==> (
#       ('e', ()),
#       ('g', ('e',)),
#       ('n', ()),
#       ('x', ('n', 'g')),
#     )
``````

### `sample`

View source

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` 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

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 `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

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

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

Unnormalized log probability density/mass function.

The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.) can be called either by passing a single structure of tensors or by using named args for each part of the joint distribution state. For example,

``````jd = tfd.JointDistributionSequential([
tfd.Normal(0., 1.),
lambda z: tfd.Normal(z, 1.)
], validate_args=True)
jd.dtype
# ==> [tf.float32, tf.float32]
z, x = sample = jd.sample()
# The following calling styles are all permissable and produce the exactly
# the same output.
assert (jd.unnormalized_log_prob(sample) ==
jd.unnormalized_log_prob(value=sample) ==
jd.unnormalized_log_prob(z, x) ==
jd.unnormalized_log_prob(z=z, x=x) ==
jd.unnormalized_log_prob(z, x=x))

# These calling possibilities also imply that one can also use `*`
# expansion, if `sample` is a sequence:
jd.unnormalized_log_prob(*sample)
# and similarly, if `sample` is a map, one can use `**` expansion:
jd.unnormalized_log_prob(**sample)
``````

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

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

Notice that in the first call, `[4.]` is interpreted as a list of one scalar while in the second call the input is a scalar. Hence both inputs result in identical scalar outputs. If we wanted to pass an explicit vector to the `Exponential` component---creating a vector-shaped batch of `unnormalized_log_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

Unnormalized log probability density/mass function.

Args
`value` `list` of `Tensor`s in `distribution_fn` order for which we compute the `unnormalized_log_prob_parts` and to parameterize other ("downstream") distributions.
`name` name prepended to ops created by this function. Default value: `"unnormalized_log_prob_parts"`.

Returns
`unnormalized_log_prob_parts` a `tuple` of `Tensor`s representing the `unnormalized_log_prob` for each `distribution_fn` evaluated at each corresponding `value`.

### `unnormalized_prob_parts`

View source

Unnormalized probability density/mass function.

Args
`value` `list` of `Tensor`s in `distribution_fn` order for which we compute the `unnormalized_prob_parts` and to parameterize other ("downstream") distributions.
`name` name prepended to ops created by this function. Default value: `"unnormalized_prob_parts"`.

Returns
`unnormalized_prob_parts` a `tuple` of `Tensor`s representing the `unnormalized_prob` for each `distribution_fn` evaluated at each corresponding `value`.

### `variance`

View source

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`

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`s and `tf.Tensor`s 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__`

View source

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

[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]