tfp.experimental.distributions.MultiTaskGaussianProcessRegressionModel

Posterior predictive in a conjugate Multi-task GP regression model.

Inherits From: AutoCompositeTensorDistribution, Distribution, AutoCompositeTensor

tfp.experimental.distributions.MultiTaskGaussianProcessRegressionModel(
    kernel,
    observation_index_points,
    observations,
    observations_is_missing=None,
    index_points=None,
    mean_fn=None,
    observation_noise_variance=None,
    predictive_noise_variance=None,
    cholesky_fn=None,
    validate_args=False,
    allow_nan_stats=False,
    name='MultiTaskGaussianProcessRegressionModelWithCholesky',
    _flattened_conditional_mean_fn=None,
    _observation_scale=None
)

Args
`kernel`	`MultiTaskKernel`-like instance representing the GP's covariance function.
`observation_index_points`	(Nested) `float` `Tensor` representing finite collection, or batch of collections, of points in the index set for which some data has been observed. Shape (of each nested component) has the form `[b1, ..., bB, e, f1, ..., fF]` where `F` is the number of feature dimensions and must equal `kernel.feature_ndims` (or its corresponding nested component), and `e` is the number (size) of index points in each batch. `[b1, ..., bB, e]` must be broadcastable with the shape of `observations`, and `[b1, ..., bB]` must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc).
`observations`	`float` `Tensor` representing collection, or batch of collections, of observations corresponding to `observation_index_points`. Shape has the form `[b1, ..., bB, e, t]`, which must be broadcastable with the batch and example shapes of `observation_index_points`. The batch shape `[b1, ..., bB]` must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc.).
`observations_is_missing`	`bool` `Tensor` of shape `[..., e, t]`, representing a batch of boolean masks. When `observations_is_missing` is not `None`, this distribution is conditioned only on the observations for which the corresponding elements of `observations_is_missing` are `False`.
`index_points`	(Nested) `float` `Tensor` representing finite collection, or batch of collections, of points in the index set over which the GP is defined. Shape (or shape of each nested component) has the form `[b1, ..., bB, e, f1, ..., fF]` where `F` is the number of feature dimensions and must equal `kernel.feature_ndims` (or its corresponding nested component) and `e` is the number (size) of index points in each batch. Ultimately this distribution corresponds to an `e`-dimensional multivariate normal. The batch shape must be broadcastable with `kernel.batch_shape`.
`mean_fn`	Python `callable` that acts on `index_points` to produce a (batch of) collection of mean values at `index_points`. Takes a (nested) `Tensor` of shape `[b1, ..., bB, e, f1, ..., fF]` and returns a `Tensor` whose shape is broadcastable with `[b1, ..., bB, e, t]`, where `t` is the number of tasks.
`observation_noise_variance`	`float` `Tensor` representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc.). Default value: `None`
`predictive_noise_variance`	`float` `Tensor` representing the variance in the posterior predictive model. If `None`, we simply re-use `observation_noise_variance` for the posterior predictive noise. If set explicitly, however, we use this value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
`cholesky_fn`	Callable which takes a single (batch) matrix argument and returns a Cholesky-like lower triangular factor. Default value: `None`, in which case `make_cholesky_with_jitter_fn(1e-6)` is used.
`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`.
`allow_nan_stats`	Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value `NaN` to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. Default value: `False`.
`name`	Python `str` name prefixed to Ops created by this class. Default value: 'MultiTaskGaussianProcessRegressionModel'.
`_flattened_conditional_mean_fn`	Internal parameter -- do not use.
`_observation_scale`	Internal parameter -- do not use.

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_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.
`cholesky_fn`
`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`	The list or structure of lists of active shard axis names.
`index_points`
`kernel`
`mean_fn`
`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. 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.
`observation_index_points`
`observation_noise_variance`
`observation_scale`
`observations`
`observations_is_missing`
`parameters`	Dictionary of parameters used to instantiate this `Distribution`.
`predictive_noise_variance`
`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: 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.
`validate_args`	Python `bool` indicating possibly expensive checks are enabled.
`variables`	Sequence of variables owned by this module and its submodules. 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.

Methods

`batch_shape_tensor`

View source

batch_shape_tensor(
    name='batch_shape_tensor'
)

Shape of a single sample from a single event index as a 1-D Tensor.

The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

Args
`name`	name to give to the op

Returns
`batch_shape`	`Tensor`.

`cdf`

View source

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

Cumulative distribution function.

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

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

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`

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copy(
    **override_parameters_kwargs
)

Creates a deep copy of the distribution.

Args
`**override_parameters_kwargs`	String/value dictionary of initialization arguments to override with new values.

Returns
`distribution`	A new instance of `type(self)` initialized from the union of self.parameters and override_parameters_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`.

`covariance`

View source

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`

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cross_entropy(
    other, name='cross_entropy'
)

Computes the (Shannon) cross entropy.

Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shannon) cross entropy is defined as:

H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)

where F denotes the support of the random variable X ~ P.

Args
`other`	`tfp.distributions.Distribution` 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

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

Shannon entropy in nats.

`event_shape_tensor`

View source

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

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 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`

View source

@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

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_sample_and_log_prob`

View source

experimental_sample_and_log_prob(
    sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
)

Samples from this distribution and returns the log density of the sample.

The default implementation simply calls sample and log_prob:

def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
  x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
  return x, self.log_prob(x, **kwargs)

However, some subclasses may provide more efficient and/or numerically stable implementations.

Args
`sample_shape`	integer `Tensor` desired shape of samples to draw. Default value: `()`.
`seed`	PRNG seed; see `tfp.random.sanitize_seed` for details. Default value: `None`.
`name`	name to give to the op. Default value: `'sample_and_log_prob'`.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`samples`	a `Tensor`, or structure of `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

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`.

`is_scalar_event`

View source

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`.

`kl_divergence`

View source

kl_divergence(
    other, name='kl_divergence'
)

Computes the Kullback--Leibler divergence.

Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as:

KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]

where F denotes the support of the random variable X ~ p, H[., .] denotes (Shannon) cross entropy, and H[.] denotes (Shannon) entropy.

Args
`other`	`tfp.distributions.Distribution` 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_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

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

Log probability density/mass function.

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
`log_prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`log_survival_function`

View source

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

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

Mean.

`mode`

View source

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

Mode.

`param_shapes`

View source

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

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

This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample().

Subclasses should override class method _param_shapes.

Args
`sample_shape`	`Tensor` or python list/tuple. Desired shape of a call to `sample()`.
`name`	name to prepend ops with.

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

`param_static_shapes`

View source

@classmethod
param_static_shapes(
    sample_shape
)

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

This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically.

Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

Args
`sample_shape`	`TensorShape` or python list/tuple. Desired shape of a call to `sample()`.

Returns
`dict` of parameter name to `TensorShape`.

Raises
`ValueError`	if `sample_shape` is a `TensorShape` and is not fully defined.

`parameter_properties`

View source

@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.

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`.

`precompute_regression_model`

View source

@staticmethod
precompute_regression_model(
    kernel,
    observation_index_points,
    observations,
    observations_is_missing=None,
    index_points=None,
    observation_noise_variance=None,
    predictive_noise_variance=None,
    mean_fn=None,
    cholesky_fn=None,
    validate_args=False,
    allow_nan_stats=False,
    name='PrecomputedMultiTaskGaussianProcessRegressionModel',
    _precomputed_divisor_matrix_cholesky=None,
    _precomputed_solve_on_observation=None
)

Returns a MTGaussianProcessRegressionModel with precomputed quantities.

This differs from the constructor by precomputing quantities associated with observations in a non-tape safe way. index_points is the only parameter that is allowed to vary (i.e. is a Variable / changes after initialization).

Specifically:

We make observation_index_points and observations mandatory parameters.
We precompute kernel(observation_index_points, observation_index_points) along with any other associated quantities relating to the kernel, observations and observation_index_points.

A typical usecase would be optimizing kernel hyperparameters for a MultiTaskGaussianProcess, and computing the posterior predictive with respect to those optimized hyperparameters and observation / index-points pairs.

Args
`kernel`	`PositiveSemidefiniteKernel`-like instance representing the GP's covariance function.
`observation_index_points`	(Nested) `float` `Tensor` representing finite collection, or batch of collections, of points in the index set for which some data has been observed. Shape (or shape of each nested component) has the form `[b1, ..., bB, e, f1, ..., fF]` where `F` is the number of feature dimensions and must equal `kernel.feature_ndims` (or its corresponding nested component), and `e` is the number (size) of index points in each batch. `[b1, ..., bB, e]` must be broadcastable with the shape of `observations`, and `[b1, ..., bB]` must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc). The default value is `None`, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance `predictive_noise_variance`).
`observations`	`float` `Tensor` representing collection, or batch of collections, of observations corresponding to `observation_index_points`. Shape has the form `[b1, ..., bB, e, t]` The batch shape `[b1, ..., bB]` must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc.). The default value is `None`, which corresponds to the empty set of observations, and simply results in the prior predictive model (a GP with noise of variance `predictive_noise_variance`).
`observations_is_missing`	`bool` `Tensor` of shape `[..., e]`, representing a batch of boolean masks. When `observations_is_missing` is not `None`, the returned distribution is conditioned only on the observations for which the corresponding elements of `observations_is_missing` are `True`.
`index_points`	(Nested) `float` `Tensor` representing finite collection, or batch of collections, of points in the index set over which the GP is defined. Shape (or shape of each nested component) has the form `[b1, ..., bB, e, f1, ..., fF]` where `F` is the number of feature dimensions and must equal `kernel.feature_ndims` (or its corresponding nested component) and `e` is the number (size) of index points in each batch. Ultimately this distribution corresponds to an `e`-dimensional multivariate normal. The batch shape must be broadcastable with `kernel.batch_shape` and any batch dims yielded by `mean_fn`.
`observation_noise_variance`	`float` `Tensor` representing the variance of the noise in the Normal likelihood distribution of the model. May be batched, in which case the batch shape must be broadcastable with the shapes of all other batched parameters (`kernel.batch_shape`, `index_points`, etc.). Default value: `None`
`predictive_noise_variance`	`float` `Tensor` representing the variance in the posterior predictive model. If `None`, we simply re-use `observation_noise_variance` for the posterior predictive noise. If set explicitly, however, we use this value. This allows us, for example, to omit predictive noise variance (by setting this to zero) to obtain noiseless posterior predictions of function values, conditioned on noisy observations.
`mean_fn`	Python `callable` that acts on `index_points` to produce a collection, or batch of collections, of mean values at `index_points`. Takes a (nested) `Tensor` of shape `[b1, ..., bB, e, f1, ..., fF]` and returns a `Tensor` whose shape is broadcastable with `[b1, ..., bB, e, t]`. Default value: `None` implies the constant zero function.
`cholesky_fn`	Callable which takes a single (batch) matrix argument and returns a Cholesky-like lower triangular factor. Default value: `None`, in which case `make_cholesky_with_jitter_fn` is used with the `jitter` parameter.
`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`.
`allow_nan_stats`	Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value `NaN` to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. Default value: `False`.
`name`	Python `str` name prefixed to Ops created by this class. Default value: 'PrecomputedGaussianProcessRegressionModel'.
`_precomputed_divisor_matrix_cholesky`	Internal parameter -- do not use.
`_precomputed_solve_on_observation`	Internal parameter -- do not use.

Returns An instance of MultiTaskGaussianProcessRegressionModel with precomputed quantities associated with observations.

`prob`

View source

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

Probability density/mass function.

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
`prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`quantile`

View source

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

Quantile function. Aka 'inverse cdf' or 'percent point function'.

Given random variable X and p in [0, 1], the quantile is:

quantile(p) := x such that P[X <= x] == p

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`quantile`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`sample`

View source

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.

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`.

`stddev`

View source

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

Standard deviation.

Standard deviation is defined as,

stddev = E[(X - E[X])**2]**0.5

where X is the random variable associated with this distribution, 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(
    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

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

Potentially unnormalized log probability density/mass function.

This function is similar to log_prob, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls log_prob.

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
`unnormalized_log_prob`	a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`.

`variance`

View source

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

Variance.

Variance is defined as,

Var = E[(X - E[X])**2]

where X is the random variable associated with this distribution, 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.Variables and tf.Tensors whose names included the module name:

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

Args
`method`	The method to wrap.

Returns
The original method wrapped such that it enters the module's name scope.

`getitem`

View source

__getitem__(
    slices
)

Slices the batch axes of this distribution, returning a new instance.

b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape  # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape  # => [3, 1, 5, 2, 4]

x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.batch_shape  # => [4, 5, 3]
mvn.event_shape  # => [2]
mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
mvn2.batch_shape  # => [4, 2, 3, 1]
mvn2.event_shape  # => [2]

Args
`slices`	slices from the [] operator

Returns
`dist`	A new `tfd.Distribution` instance with sliced parameters.

`iter`

View source

__iter__()

tfp.experimental.distributions.MultiTaskGaussianProcessRegressionModel

Args

Attributes

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

experimental_default_event_space_bijector

experimental_fit

experimental_local_measure

experimental_sample_and_log_prob

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

parameter_properties

precompute_regression_model

Specifically:

prob

quantile

sample

stddev

survival_function

unnormalized_log_prob

variance

with_name_scope

__getitem__

__iter__

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`experimental_default_event_space_bijector`

`experimental_fit`

`experimental_local_measure`

`experimental_sample_and_log_prob`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`parameter_properties`

`precompute_regression_model`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`unnormalized_log_prob`

`variance`

`with_name_scope`

`getitem`

`iter`