The exponential family of Markov chains and its information geometry

Abstract

We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of information geometry is effectively applied to our framework, which enables us to characterize the divergence rate of Markov chain from a differential geometric viewpoint.

This work was presented in the 28th Symposium on Information Theory and Its Applications (SITA2005) in 2005

Cited by in corpus (2)

• Finite-length Analysis on Tail probability for Markov Chain and Application to Simple Hypothesis Testing
• Information Geometry Approach to Parameter Estimation in Markov Chains