--- res: bibo_abstract: - In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost. The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a suboptimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Bernhard foaf_name: Geiger, Bernhard foaf_surname: Geiger - foaf_Person: foaf_givenName: Tatjana foaf_name: Petrov, Tatjana foaf_surname: Petrov foaf_workInfoHomepage: http://www.librecat.org/personId=3D5811FC-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9041-0905 - foaf_Person: foaf_givenName: Gernot foaf_name: Kubin, Gernot foaf_surname: Kubin - foaf_Person: foaf_givenName: Heinz foaf_name: Koeppl, Heinz foaf_surname: Koeppl bibo_doi: 10.1109/TAC.2014.2364971 bibo_issue: '4' bibo_volume: 60 dct_date: 2015^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0018-9286 dct_language: eng dct_publisher: IEEE@ dct_title: Optimal Kullback-Leibler aggregation via information bottleneck@ ...