|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution_sequential.py#L726-L747) | Joint distribution parameterized by distribution-making functions. Inherits From: [`JointDistribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution), [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) tfp.distributions.JointDistributionSequential( model, batch_ndims=None, use_vectorized_map=False, validate_args=False, experimental_use_kahan_sum=False, name=None ) ### Used in the notebooks | Used in the tutorials | |---| | - [Eight schools](https://www.tensorflow.org/probability/examples/Eight_Schools) | This distribution enables both sampling and joint probability computation from a single model specification. A joint distribution is a collection of possibly interdependent distributions. Like `tf_keras.Sequential`, the `JointDistributionSequential` can be specified via a `list` of functions (each responsible for making a [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution)-like instance). Unlike `tf_keras.Sequential`, each function can depend on the output of all previous elements rather than only the immediately previous. #### Mathematical Details The `JointDistributionSequential` implements the chain rule of probability. That is, the probability function of a length-`d` vector `x` is, p(x) = prod{ p(x[i] | x[:i]) : i = 0, ..., (d - 1) } The `JointDistributionSequential` is parameterized by a `list` comprised of either: 1. [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution)-like instances or, 2. `callable`s which return a [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution)-like instance. Each `list` element implements the `i`-th *full conditional distribution* , `p(x[i] | x[:i])`. The "conditioned on" elements are represented by the `callable`'s required arguments. Directly providing a `Distribution`-like instance is a convenience and is semantically identical a zero argument `callable`. Denote the `i`-th `callable`s non-default arguments as `args[i]`. Since the `callable` is the conditional manifest, `0 <= len(args[i]) <= i - 1`. When `len(args[i]) < i - 1`, the `callable` only depends on a subset of the previous distributions, specifically those at indexes: `range(i - 1, i - 1 - num_args[i], -1)`. (See "Examples" and "Discussion" for why the order is reversed.) **Name resolution** : `The names of`JointDistributionSequential`components are defined by explicit`name`arguments passed to distributions (`tfd.Normal(0., 1., name='x')`) and/or by the argument names in distribution-making functions (`lambda x: tfd.Normal(x., 1.)`). Both approaches may be used in the same distribution, as long as they are consistent; referring to a single component by multiple names will raise a`ValueError\`. Unnamed components will be assigned a dummy name. #### Examples Consider the following generative model: e ~ Exponential(rate=[100,120]) g ~ Gamma(concentration=e[0], rate=e[1]) n ~ Normal(loc=0, scale=2.) m ~ Normal(loc=n, scale=g) for i = 1, ..., 12: x[i] ~ Bernoulli(logits=m) We can code this as: tfd = tfp.distributions joint = tfd.JointDistributionSequential([ tfd.Exponential(rate=[100, 120]), # e lambda e: tfd.Gamma(concentration=e[0], rate=e[1]), # g tfd.Normal(loc=0, scale=2.), # n lambda n, g: tfd.Normal(loc=n, scale=g), # m lambda m: tfd.Sample(tfd.Bernoulli(logits=m), 12) # x ], batch_ndims=0, use_vectorized_map=True) Notice the 1:1 correspondence between "math" and "code". x = joint.sample() # ==> A length-5 list of Tensors representing a draw/realization from each # distribution. joint.log_prob(x) # ==> A scalar `Tensor` representing the total log prob under all five # distributions. joint.resolve_graph() # ==> (('e', ()), # ('g', ('e',)), # ('n', ()), # ('m', ('n', 'g')), # ('x', ('m',))) #### Discussion `JointDistributionSequential` builds each distribution in `list` order; list items must be either a: 3. `tfd.Distribution`-like instance (e.g., `e` and `n`), or a 4. Python `callable` (e.g., `g`, `m`, `x`). Regarding #1, an object is deemed "`tfd.Distribution`-like" if it has a `sample`, `log_prob`, and distribution properties, e.g., `batch_shape`, `event_shape`, `dtype`. Regarding #2, in addition to using a function (or `lambda`), supplying a TFD "`class`" is also permissible, this also being a "Python `callable`." For example, instead of writing: `lambda loc, scale: tfd.Normal(loc=loc, scale=scale)` one could have simply written `tfd.Normal`. Notice that directly providing a `tfd.Distribution`-like instance means there cannot exist a (dynamic) dependency on other distributions; it is "independent" both "computationally" and "statistically." The same is self-evidently true of zero-argument `callable`s. A distribution instance depends on other distribution instances through the distribution making function's *required arguments* . If the distribution maker has `k` required arguments then the `JointDistributionSequential` calls the maker with samples produced by the previous `k` distributions. > [!NOTE] > **Note:** **maker arguments are provided in reverse order** of the previous elements in the list. In the example, notice that `m` depends on `n` and `g` in this order. The order is reversed for convenience. We reverse arguments under the heuristic observation that many graphical models have chain-like dependencies which are self-evidently topologically sorted from the human cognitive process of postulating the generative process. By feeding the previous num required args in reverse order we (often) enable a simpler maker function signature. If the maker needs to depend on distribution previous to one which is not a dependency, one must use a dummy arg, to "gobble up" the unused dependency, e.g., `lambda _ignore, actual_dependency: SomeDistribution(actual_dependency)`. > [!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 anything which is `list`-like, e.g., a `list` or `tuple` of `distribution` makers. Accordingly `joint.event_shape` returns a `list`-like structure of `TensorShape`s for each of the distributions' event shapes and `joint.event_shape_tensor()` returns a `list`-like structure of `Tensor`s for each of the distributions' event shapes. > [!NOTE] > **Note:** If a `JointDistributionSequential` instance contains a `callable` that closes over a `Tensor`, the `JointDistributionSequential` cannot cross the boundary of a [`tf.function`](https://www.tensorflow.org/api_docs/python/tf/function). (If this behavior is necessary, an instance of `_JointDistributionSequential` may be used instead, at the expense of extra [`tf.function`](https://www.tensorflow.org/api_docs/python/tf/function) retracing.) #### Vectorized sampling and model evaluation When a joint distribution's `sample` method is called with a `sample_shape` (or the `log_prob` method is called on an input with multiple sample dimensions) the model must be equipped to handle additional batch dimensions. This may be done manually, or automatically by passing `use_vectorized_map=True`. Manual vectorization has historically been the default, but we now recommend that most users enable automatic vectorization unless they are affected by a specific issue; some known issues are listed below. When using manually-vectorized joint distributions, each operation in the model must account for the possibility of batch dimensions in Distributions and their samples. By contrast, auto-vectorized models need only describe a *single* sample from the joint distribution; any batch evaluation is automated as required using [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map) (`vmap` in JAX). In many cases this allows for significant simplications. For example, the following manually-vectorized `tfd.JointDistributionSequential` model: model = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), tfd.Normal(0., 1.), lambda y, x: tfd.Normal(x[..., :2] + y[..., tf.newaxis], 1.) ]) can be written in auto-vectorized form as model = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), tfd.Normal(0., 1.), lambda y, x: tfd.Normal(x[:2] + y, 1.) ], use_vectorized_map=True) in which we were able to avoid explicitly accounting for batch dimensions when indexing and slicing computed quantities in the third line. **Known limitations of automatic vectorization:** - A small fraction of TensorFlow ops are unsupported; models that use an unsupported op will raise an error and must be manually vectorized. - Sampling large batches may be slow under automatic vectorization because TensorFlow's stateless samplers are currently converted using a non-vectorized `while_loop`. This limitation applies only in TensorFlow; vectorized samplers in JAX should be approximately as fast as manually vectorized code. - Calling `sample_distributions` with nontrivial `sample_shape` will raise an error if the model contains any distributions that are not registered as CompositeTensors (TFP's basic distributions are usually fine, but support for wrapper distributions like `tfd.Sample` is a work in progress). #### Batch semantics and (log-)densities **tl;dr:** pass `batch_ndims=0` unless you have a good reason not to. Joint distributions now support 'auto-batching' semantics, in which the distribution's batch shape is derived by broadcasting the leftmost `batch_ndims` dimensions of its components' batch shapes. All remaining dimensions are considered to form a single 'event' of the joint distribution. If `batch_ndims==0`, then the joint distribution has batch shape `[]`, and all component dimensions are treated as event shape. For example, the model jd = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), lambda x: tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2])) ], batch_ndims=0) creates a joint distribution with batch shape `[]` and event shape `([3], [3, 2])`. The log-density of a sample always has shape `batch_shape`, so this guarantees that `jd.log_prob(jd.sample())` will evaluate to a scalar value. We could alternately construct a joint distribution with batch shape `[3]` and event shape `([], [2])` by setting `batch_ndims=1`, in which case `jd.log_prob(jd.sample())` would evaluate to a value of shape `[3]`. Setting `batch_ndims=None` recovers the 'classic' batch semantics (currently still the default for backwards-compatibility reasons), in which the joint distribution's `log_prob` is computed by naively summing log densities from the component distributions. Since these component densities have shapes equal to the batch shapes of the individual components, to avoid broadcasting errors it is usually necessary to construct the components with identical batch shapes. For example, the component distributions in the model above have batch shapes of `[3]` and `[3, 2]` respectively, which would raise an error if summed directly, but can be aligned by wrapping with `tfd.Independent`, as in this model: jd = tfd.JointDistributionSequential([ tfd.Normal(0., tf.ones([3])), lambda x: tfd.Independent(tfd.Normal(x[..., tf.newaxis], tf.ones([3, 2])), reinterpreted_batch_ndims=1) ], batch_ndims=None) Here the components both have batch shape `[3]`, so `jd.log_prob(jd.sample())` returns a value of shape `[3]`, just as in the `batch_ndims=1` case above. In fact, auto-batching semantics are equivalent to implicitly wrapping each component `dist` as `tfd.Independent(dist, reinterpreted_batch_ndim=(dist.batch_shape.ndims - jd.batch_ndims))`; the only vestigial difference is that under auto-batching semantics, the joint distribution has a single batch shape `[3]`, while under the classic semantics the value of `jd.batch_shape` is a *structure* of the component batch shapes `([3], [3])`. Such structured batch shapes will be deprecated in the future, since they are inconsistent with the definition of batch shapes used elsewhere in TFP. #### References \[1\] Dan Piponi, Dave Moore, and Joshua V. Dillon. Joint distributions for TensorFlow Probability. *arXiv preprint arXiv:2001.11819*_, 1. If every element of `model` is a `CompositeTensor` or a callable, the resulting `JointDistributionSequential` is a `CompositeTensor`.Otherwise, a non-`CompositeTensor` `_JointDistributionSequential` instance is created.


| ## Args || |---|---| | `model` | Python list of either tfd.Distribution instances and/or lambda functions which take the `k` previous distributions and returns a new tfd.Distribution instance. | | `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: `None`. | | `use_vectorized_map` | Python `bool`. Whether to use [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/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: `False`. | | `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`](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_kahan_sum). This argument has no effect if `batch_ndims is None`. Default value: `False`. | | `name` | The name for ops managed by the distribution. Default value: `None` (i.e., `"JointDistributionSequential"`). |



| ## 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. | | `model` |

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


| 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. Additional documentation from `_JointDistributionSequential`: 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. `other` types with built-in registrations: `JointDistributionNamed`, `JointDistributionNamedAutoBatched`, `JointDistributionSequential`, `JointDistributionSequentialAutoBatched`


| 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`. |
### `resolve_graph` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/distributions/joint_distribution_sequential.py#L424-L463) resolve_graph( distribution_names=None, leaf_name='x' ) 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](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/joint_distribution_sequential.py#L516-L565) __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__()