LowRankMultivariateNormal

class tensorplay.distributions.LowRankMultivariateNormal(loc: Tensor, cov_factor: Tensor, cov_diag: Tensor, validate_args: bool | None = None)[source]

Creates a multivariate normal distribution with covariance matrix having a low-rank form parameterized by cov_factor and cov_diag:

covariance_matrix = cov_factor @ cov_factor.T + cov_diag

Example

>>> # xdoctest: +REQUIRES(env:TENSORPLAY_DOCTEST_LAPACK)
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = LowRankMultivariateNormal(
...     tensorplay.zeros(2), tensorplay.tensor([[1.0], [0.0]]), tensorplay.ones(2)
... )
>>> m.sample()  # normally distributed with mean=`[0,0]`, cov_factor=`[[1],[0]]`, cov_diag=`[1,1]`
tensor([-0.2102, -0.5429])

Parameters:

• loc (Tensor) – mean of the distribution with shape batch_shape + event_shape

• cov_factor (Tensor) – factor part of low-rank form of covariance matrix with shape batch_shape + event_shape + (rank,)

• cov_diag (Tensor) – diagonal part of low-rank form of covariance matrix with shape batch_shape + event_shape

Note

The computation for determinant and inverse of covariance matrix is avoided when cov_factor.shape[1] << cov_factor.shape[0] thanks to Woodbury matrix identity and matrix determinant lemma. Thanks to these formulas, we just need to compute the determinant and inverse of the small size “capacitance” matrix:

capacitance = I + cov_factor.T @ inv(cov_diag) @ cov_factor

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.

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.