Wishart

class tensorplay.distributions.Wishart(df: Tensor | bool | int | float, covariance_matrix: Tensor | None = None, precision_matrix: Tensor | None = None, scale_tril: Tensor | None = None, validate_args: bool | None = None)[source]

Creates a Wishart distribution parameterized by a symmetric positive definite matrix $\Sigma$, or its Cholesky decomposition $\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top$

Example

>>> # xdoctest: +SKIP("FIXME: scale_tril must be at least two-dimensional")
>>> m = Wishart(tensorplay.Tensor([2]), covariance_matrix=tensorplay.eye(2))
>>> m.sample()  # Wishart distributed with mean=`df * I` and
>>> # variance(x_ij)=`df` for i != j and variance(x_ij)=`2 * df` for i == j

Parameters:

• df (float or Tensor) – real-valued parameter larger than the (dimension of Square matrix) - 1

• covariance_matrix (Tensor) – positive-definite covariance matrix

• precision_matrix (Tensor) – positive-definite precision matrix

• scale_tril (Tensor) – lower-triangular factor of covariance, with positive-valued diagonal

Note

Only one of covariance_matrix or precision_matrix or scale_tril can be specified. Using scale_tril will be more efficient: all computations internally are based on scale_tril. If covariance_matrix or precision_matrix is passed instead, it is only used to compute the corresponding lower triangular matrices using a Cholesky decomposition. ‘tensorplay.distributions.LKJCholesky’ is a restricted Wishart distribution.[1]

References

[1] Wang, Z., Wu, Y. and Chu, H., 2018. On equivalence of the LKJ distribution and the restricted Wishart distribution. [2] Sawyer, S., 2007. Wishart Distributions and Inverse-Wishart Sampling. [3] Anderson, T. W., 2003. An Introduction to Multivariate Statistical Analysis (3rd ed.). [4] Odell, P. L. & Feiveson, A. H., 1966. A Numerical Procedure to Generate a Sample Covariance Matrix. JASA, 61(313):199-203. [5] Ku, Y.-C. & Bloomfield, P., 2010. Generating Random Wishart Matrices with Fractional Degrees of Freedom in OX.

property batch_shape: Size

Returns the shape over which parameters are batched.

cdf(value: Tensor) → Tensor

Returns the cumulative density/mass function evaluated at value.

Parameters:

value (Tensor)

enumerate_support(expand: bool = True) → Tensor

Returns tensor containing all values supported by a discrete distribution. The result will enumerate over dimension 0, so the shape of the result will be (cardinality,) + batch_shape + event_shape (where event_shape = () for univariate distributions).

Note that this enumerates over all batched tensors in lock-step [[0, 0], [1, 1], …]. With expand=False, enumeration happens along dim 0, but with the remaining batch dimensions being singleton dimensions, [[0], [1], ...

To iterate over the full Cartesian product use itertools.product(m.enumerate_support()).

Parameters:

expand (bool) – whether to expand the support over the batch dims to match the distribution’s batch_shape.

Returns:

Tensor iterating over dimension 0.

property event_shape: Size

Returns the shape of a single sample (without batching).

icdf(value: Tensor) → Tensor

Returns the inverse cumulative density/mass function evaluated at value.

Parameters:

value (Tensor)

perplexity() → Tensor

Returns perplexity of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

rsample(sample_shape: Size | Sequence[int] = (), max_try_correction=None) → Tensor[source]

Warning

In some cases, sampling algorithm based on Bartlett decomposition may return singular matrix samples. Several tries to correct singular samples are performed by default, but it may end up returning singular matrix samples. Singular samples may return -inf values in .log_prob(). In those cases, the user should validate the samples and either fix the value of df or adjust max_try_correction value for argument in .rsample accordingly.

sample(sample_shape: Size | Sequence[int] = ()) → Tensor

Generates a sample_shape shaped sample or sample_shape shaped batch of samples if the distribution parameters are batched.

sample_n(n: int) → Tensor

Generates n samples or n batches of samples if the distribution parameters are batched.

static set_default_validate_args(value: bool) → None

Sets whether validation is enabled or disabled.

The default behavior mimics Python’s assert statement: validation is on by default, but is disabled if Python is run in optimized mode (via python -O). Validation may be expensive, so you may want to disable it once a model is working.

Parameters:

value (bool) – Whether to enable validation.

property stddev: Tensor

Returns the standard deviation of the distribution.