bregman.application.distribution.exponential_family package

Subpackages

Submodules

bregman.application.distribution.exponential_family.exp_family module

class bregman.application.distribution.exponential_family.exp_family.ExponentialFamilyDistribution(theta: ndarray, dimension: tuple[int, ...])

Bases: Distribution, ABC

Exponential family distribution abstract class.

Parameters:

theta – Natural parameters of the exponential family distribution.

abstract F(x: ndarray) → ndarray

\(F(x) = \log \int \exp(\theta^T t(x)) \mathrm{d}x\) normalizer.

Parameters:

x – Parameter value.

Returns:

Normalizer evaluated at parameter value x.

abstract static k(x: ndarray) → ndarray

\(k(x)\) carrier measure.

Parameters:

x – Sample space input.

Returns:

Carries measure evaluated at x.

pdf(x: ndarray) → ndarray

P.d.f. of exponential family distribution.

Parameters:

x – Sample space input.

Returns:

P.d.f. of exponential family distribution evaluated at x.

abstract static t(x: ndarray) → ndarray

\(t(x)\) sufficient statistics function.

Parameters:

x – Sample space input.

Returns:

Sufficient statistics function evaluated at x.

class bregman.application.distribution.exponential_family.exp_family.ExponentialFamilyManifold(natural_generator: Generator, expected_generator: Generator, distribution_class: type[MyExpFamDistribution], display_factory_class: type[MyDisplayPoint], dimension: int)

Bases: DistributionManifold[MyDisplayPoint, MyExpFamDistribution], Generic[MyDisplayPoint, MyExpFamDistribution], ABC

Exponential family distribution manifold.

Parameters:

distribution_class – Distribution class corresponding to the manifold.

kl_divergence(point_1: Point, point_2: Point) → ndarray

KL-Divergence of two points in an exponential family manifold.

This is equivalent to the Bregman divergence of natural or expected parameters.

Parameters:

  • point_1 – Left-sided argument of the KL-Divergence.

  • point_2 – Right-sided argument of the KL-Divergence.

Returns:

KL-Divergence between point_1 and point_2 on the exponential family manifold.

t(x: ndarray) → ndarray

\(t(x)\) sufficient statistics function.

Parameters:

x – Sample space input.

Returns:

Sufficient statistics function evaluated at x.

Module contents