The exponential family in abstract information theory

TL;DR

This paper extends the concept of exponential families using information geometry, introducing generalized divergence functions and Fisher information matrices applicable beyond traditional statistical contexts.

Contribution

It reformulates exponential families through Fisher information matrices, broadening their applicability with generalized divergence measures and information geometric methods.

Findings

Generalized divergence functions introduced

Fisher information matrix reformulated for exponential families

Applicable to diverse fields beyond statistics

Abstract

We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are those of information geometry. The context is general enough to include applications from outside statistics.