Information-Preserving Markov Aggregation

TitleInformation-Preserving Markov Aggregation
Publication TypeConference Paper
Year of Publication2013
AuthorsGeiger, B., & Temmel C.
Conference NameIEEE Information Theory Workshop (ITW)
Pages258-262
Conference LocationSeville, Spain
Abstract

We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain.

We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.
URLhttp://arxiv.org/abs/1304.0920
DOI10.1109/ITW.2013.6691265
Citation Key2733
Refereed DesignationRefereed
SPSC cross-references
Research Area: 
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