Riemannian curvature of gaussian distribution in dual coordinate system

TL;DR

This paper investigates the geometric properties like curvature and torsion of Gaussian distributions within a dual coordinate system on a Riemannian manifold, providing explicit formulas and characterizations of key invariants.

Contribution

It introduces explicit Amari formulas in the dual coordinate system and characterizes geometric invariants of Gaussian distributions on the Riemannian manifold.

Findings

Explicit formulas for Amari in dual coordinates

Characterization of geometric invariants like Fisher metric

Analysis of curvature and torsion properties

Abstract

In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this new coordinate system, which allows us to characterize existing geometric invariants, such as the dual potential function and the Fisher metric.