Higher-Order Kullback-Leibler Aggregation of Markov Chains

We consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present information-theoretic cost functions that are related to predictability and lumpability, show relations between these cost functions, and discuss heuristi...

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Bibliographic Details
Main Authors Geiger, Bernhard C, Wu, Yuchen
Format Journal Article
LanguageEnglish
Published 16.08.2016
Subjects
Computer Science - Information Theory
Mathematics - Information Theory
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Summary:We consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present information-theoretic cost functions that are related to predictability and lumpability, show relations between these cost functions, and discuss heuristics to minimize them. Our experiments suggest that the generalization to higher orders is useful for model reduction in reliability analysis and natural language processing.
DOI:10.48550/arxiv.1608.04637