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An Information-Theoretic Approach for Automatically Determining the Number of States when Aggregating Markov Chains
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.Comment: Submitted to IEEE ICASSP. arXiv admin note: substantial text overlap
with arXiv:1903.0926