An elementary introduction to information geometry

TL;DR

This survey introduces the basic differential-geometric structures of information manifolds, explaining their theoretical foundations and illustrating their applications in information sciences, providing a self-contained overview without detailed proofs.

Contribution

It offers a clear, self-contained introduction to the core concepts of information geometry, including the fundamental theorem and practical use cases.

Findings

Fundamental theorem of information geometry explained

Illustrations of information manifolds in applications

Concise introduction to differential geometry concepts

Abstract

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry, but proofs are omitted for brevity.