An Information-Theoretic Approach for Automatically Determining the Number of States when Aggregating Markov Chains
This addresses a fundamental issue in model reduction for Markov chains, which is incremental as it builds on existing aggregation methods.
The paper tackles the problem of determining the optimal number of state groups when aggregating Markov chains, showing that an information-theoretic approach balances complexity and mutual dependence to find this number automatically.
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.