Marginal Polytope of a Deformed Exponential Family

TL;DR

This paper investigates the marginal polytope associated with $ ext{phi}$-exponential families, extending the understanding of their geometric structure in finite state spaces, building on Tsallis' and Naudts' work on deformed logarithms.

Contribution

It introduces the concept of the marginal polytope for $ ext{phi}$-exponential families, expanding the geometric analysis of deformed exponential models.

Findings

Characterization of the marginal polytope in finite state spaces.

Extension of Tsallis' and Naudts' frameworks to geometric structures.

Insights into the convexity and structure of $ ext{phi}$-exponential families.

Abstract

A deformed logarithm function called $q$-logarithm has received considerable attention by physicist after its introduction by C. Tsallis. J. Naudts has proposed a generalization called $\phi$-logarithm and he has derived the basic properties of $\phi$-exponential families. In this paper we study the related notion of marginal polytope in the case of a finite state space.