# Reduction of Markov Chains using a Value-of-Information-Based Approach

## TL;DR

This paper introduces a novel information-theoretic method for reducing Markov chains by probabilistically partitioning states based on a value-of-information criterion, allowing data-driven model simplification.

## Contribution

It presents a new approach combining KL divergence and value-of-information optimization for Markov chain reduction, with a method to select the optimal number of state groups without prior knowledge.

## Key findings

- Effective probabilistic state partitioning achieved
- Data-driven parameter selection method developed
- Reduces model complexity while preserving key dynamics

## Abstract

In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative Kullback-Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the `optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.