Information geometry of warped product spaces

TL;DR

This paper explores the information geometric structure of warped product spaces, focusing on dually flat connections and characterizing specific connections on the base space, with implications for statistical models.

Contribution

It provides a detailed analysis of the information geometry of warped products, especially characterizing $ abla^{(eta)}$-connections on the base space for certain cases.

Findings

Connections on the base space are $ abla^{(eta)}$ with $eta= ext{±}1$

Characterization of connections in warped product spaces with dually flat structures

Application to statistical models involving warped products

Abstract

Information geometry is an important tool to study statistical models. There are some important examples in statistical models which are regarded as warped products. In this paper, we study information geometry of warped products. We consider the case where the warped product and its fiber space are equipped with dually flat connections and, in the particular case of a cone, characterize the connections on the base space $\mathbb{R}_{>0}$. The resulting connections turn out to be the $\alpha$-connections with $\alpha = \pm{1}$.