On Information (pseudo) Metric

TL;DR

This paper revisits the information metric, highlighting its nature as a pseudo metric on manifolds of observables, characterizing geodesics, and illustrating its computation on a diabetes dataset.

Contribution

It clarifies the geometric interpretation of the information metric on observables and provides characterizations of geodesics and a Pythagorean theorem within this framework.

Findings

Information metric is a pseudo metric on manifolds of observables.

Geodesics are characterized by boundary and independence conditions.

The metric is computed on a real dataset using infotopo.

Abstract

This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and conditional independence condition. Pythagorean theorem is given, providing in special case potentially interesting natural integer triplets. This metric is computed for illustration on Diabetes dataset using infotopo package.