Markov State Space Aggregation via the Information Bottleneck Method

Bernhard C. Geiger


Consider the problem of approximating a Markov chain by another Markov chain with a smaller state space that is obtained by partitioning the original state space. An information-theoretic cost function is proposed that is based on the relative entropy rate between the original Markov chain and a Markov chain defined by the partition. The state space aggregation problem can be sub-optimally solved by using the information bottleneck method.

Słowa kluczowe: Markov chains, state space aggregation, coarse-graining, information bottleneck, relative entropy, lumpability

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