An Information-Theoretic Approach for Automatically Determining the Number of States when Aggregating Markov Chains

TL;DR

This paper introduces an information-theoretic method for automatically selecting the optimal number of state groups in Markov chain aggregation, balancing model complexity and fidelity.

Contribution

It proposes an augmented value-of-information approach that determines the ideal number of states by balancing complexity and dependence.

Findings

The method effectively identifies the optimal number of state groups.

It balances model simplicity with capturing essential dynamics.

The approach improves upon existing aggregation techniques.

Abstract

A fundamental problem when aggregating Markov chains is the specification of the number of state groups. Too few state groups may fail to sufficiently capture the pertinent dynamics of the original, high-order Markov chain. Too many state groups may lead to a non-parsimonious, reduced-order Markov chain whose complexity rivals that of the original. In this paper, we show that an augmented value-of-information-based approach to aggregating Markov chains facilitates the determination of the number of state groups. The optimal state-group count coincides with the case where the complexity of the reduced-order chain is balanced against the mutual dependence between the original- and reduced-order chain dynamics.