Which probability distributions are supported by this skill?

The skill includes built-in implementations for Categorical and Gaussian distributions, providing the necessary Fisher Information Matrix and dually flat structures for these models.

What is the benefit of natural gradient over standard gradient descent?

Natural gradient is parameterization-invariant, meaning it finds the steepest descent on the manifold of probability distributions rather than the raw parameter space, often leading to more stable and efficient convergence.

How does this skill handle statistical divergences?

It provides a robust Divergence Suite that can calculate KL divergence, Fisher-Rao distance, Hellinger distance, and alpha-divergences to quantify the difference between statistical states.

What are m-geodesics and e-geodesics?

They are paths on a statistical manifold; m-geodesics are flat in mixture coordinates (linear combinations), while e-geodesics are flat in natural coordinates (exponential combinations).

Information Geometry

Name: Information Geometry
Author: plurigrid

byplurigrid

•

数据科学与机器学习

Implements Fisher-Rao metrics and natural gradient optimization on statistical manifolds for advanced probabilistic modeling.

The Information Geometry skill provides a specialized framework for treating probability distributions as points on a Riemannian manifold. By utilizing the Fisher-Rao metric, it enables developers to perform natural gradient descent—a powerful, parameterization-invariant optimization technique—and compute complex statistical divergences such as KL, Hellinger, and Renyi. This skill is essential for researchers and engineers working with exponential families, active inference, or high-dimensional signal processing where standard Euclidean optimization is insufficient.

主要功能

017 GitHub stars

02Geodesic tracing for mixture (m-connection) and exponential (e-connection) paths

03Comprehensive divergence suite including KL, Fisher-Rao, and Hellinger

04Support for dually flat structures and manifold curvature analysis

05Fisher Information Matrix computation for categorical and Gaussian models

06Natural gradient descent for parameterization-invariant optimization

使用场景

01Measuring the geodesic distance between probability distributions in statistical modeling

02Analyzing information flow and manifold curvature in BCI or signal processing pipelines

03Optimizing deep learning models using natural gradient descent for faster convergence

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi information-geometry

For use in Claude.ai and ChatGPT

Download Skill