LKJCholesky

class tensorplay.distributions.LKJCholesky(dim: int, concentration: Tensor | float = 1.0, validate_args: bool | None = None)[source]

LKJ distribution for lower Cholesky factor of correlation matrices. The distribution is controlled by concentration parameter $\eta$ to make the probability of the correlation matrix $M$ generated from a Cholesky factor proportional to $\det(M)^{\eta - 1}$. Because of that, when concentration == 1, we have a uniform distribution over Cholesky factors of correlation matrices:

L ~ LKJCholesky(dim, concentration)
X = L @ L' ~ LKJCorr(dim, concentration)

Note that this distribution samples the Cholesky factor of correlation matrices and not the correlation matrices themselves and thereby differs slightly from the derivations in [1] for the LKJCorr distribution. For sampling, this uses the Onion method from [1] Section 3.

Example:

>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> l = LKJCholesky(3, 0.5)
>>> l.sample()  # l @ l.T is a sample of a correlation 3x3 matrix
tensor([[ 1.0000,  0.0000,  0.0000],
        [ 0.3516,  0.9361,  0.0000],
        [-0.1899,  0.4748,  0.8593]])

Parameters:

• dimension (dim) – dimension of the matrices

• concentration (float or Tensor) – concentration/shape parameter of the distribution (often referred to as eta)

References

[1] Generating random correlation matrices based on vines and extended onion method (2009), Daniel Lewandowski, Dorota Kurowicka, Harry Joe. Journal of Multivariate Analysis. 100. 10.1016/j.jmva.2009.04.008

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)

entropy() → Tensor

Returns entropy of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

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)

property mean: Tensor

Returns the mean of the distribution.

property mode: Tensor

Returns the mode of the distribution.

perplexity() → Tensor

Returns perplexity of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

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

Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized 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.

property variance: Tensor

Returns the variance of the distribution.