Information Geometry

Introduction

Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions.

Contents

Conjugate Connections
Statistical Manifold
Fundamental Theorem of Information Geometry
Divergence and Bregman Geometry
Classification of Divergences
Fisher Information Metric
Monotonicity of Fisher-Rao Metric
Principle Component Analysis
Autoencoders

References and Useful Resource

• John Baez, Information Geometry
• Frank Nielsen, An Elementary Introduction to Information Geometry