On Determining and Qualifying the Number of Superstates in Aggregation of Markov Chains

Srivastava, Amber; Velicheti, Raj K.; Salapaka, Srinivasa M.

doi:10.48550/arxiv.2010.05341

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Coarse Graining-based Markov Aggregation1

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2022

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“…Nevertheless, the authors of [44] and [54] proposed determining | X | by looking for "elbows" or minima in their respective objective functions. For the approach in [70], [71], the size of the aggregated state space was connected to the heterogeneity of aggregate states [73]. The authors of [74], in turn, proposed to modify the value-of-information criterion to prevent the aggregated state space from becoming too large.…”

Section: Coarse Graining-based Markov Aggregationmentioning

confidence: 99%

Information-Theoretic Reduction of Markov Chains

Geiger¹

2022

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We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a smaller state space that is informative about certain quantities of interest. The second part considers Markov chain model reduction, which focuses on replacing the original Markov model by a simplified one that yields similar behavior as the original Markov model. We discuss the practical relevance of both approaches in the field of knowledge discovery and data mining by formulating problems of unsupervised machine learning as reduction problems of Markov chains. Finally, we briefly discuss the concept of lumpability, the phenomenon when a coarse graining yields a reduced Markov model.

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Section: Coarse Graining-based Markov Aggregationmentioning

confidence: 99%

Information-Theoretic Reduction of Markov Chains

Geiger¹

2022

Preprint

View full text Add to dashboard Cite

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On Determining and Qualifying the Number of Superstates in Aggregation of Markov Chains

Cited by 1 publication

References 0 publications

Information-Theoretic Reduction of Markov Chains

Information-Theoretic Reduction of Markov Chains

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