Module information_geometry 

Information geometry and statistical manifolds.

This module provides tools for studying the geometry of families of probability distributions, including Fisher information, geodesics, natural gradients, and divergence measures.

Structs

AlphaGeometry

α-geometry: a one-parameter family of affine connections on statistical manifolds, introduced by Amari.

ExponentialFamily

An exponential family of distributions.

GaussianManifold

The manifold of univariate Gaussian distributions parameterized by (μ, σ) with σ > 0.

InformationProjection

Information projection onto an exponential family.

StatisticalManifold

A statistical manifold: a smooth manifold whose points are probability distributions parameterized by dim real parameters.

Functions

differential_entropy

Estimate differential entropy h(X) = −∫ p(x) log p(x) dx using kernel density estimation (Gaussian KDE).

mutual_information_estimator

Estimate mutual information I(X;Y) using the k-nearest-neighbour (kNN) method (Kraskov–Stögbauer–Grassberger estimator).

natural_gradient

Compute the natural gradient F^{-1} g given Fisher matrix fisher and Euclidean gradient grad.