Geiger, B. C. ; Petrov, T. ; Kubin, G. ; Koeppl, H. (2015)
Optimal Kullback-Leibler Aggregation via Information Bottleneck.
In: IEEE Transactions on Automatic Control, 60 (4)
Artikel, Bibliographie
Kurzbeschreibung (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 the a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires exhaustive search among all state space partitions, and exact evaluation of the reduction cost for each candidate partition. In our approach, we optimize an upper bound on the reduction cost instead of the exact cost; The proposed upper bound is easy to compute and it is tight in the case when the original chain is lumpable with respect to the partition. Then, we express the problem in form of information bottleneck optimization, and we propose the agglomerative information bottleneck algorithm for finding a locally optimal solution. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2015 |
| Autor(en): | Geiger, B. C. ; Petrov, T. ; Kubin, G. ; Koeppl, H. |
| Art des Eintrags: | Bibliographie |
| Titel: | Optimal Kullback-Leibler Aggregation via Information Bottleneck |
| Sprache: | Englisch |
| Publikationsjahr: | 2015 |
| Verlag: | IEEE |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | IEEE Transactions on Automatic Control |
| Jahrgang/Volume einer Zeitschrift: | 60 |
| (Heft-)Nummer: | 4 |
| URL / URN: | http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6... |
| Zugehörige Links: | |
| Kurzbeschreibung (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 the a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires exhaustive search among all state space partitions, and exact evaluation of the reduction cost for each candidate partition. In our approach, we optimize an upper bound on the reduction cost instead of the exact cost; The proposed upper bound is easy to compute and it is tight in the case when the original chain is lumpable with respect to the partition. Then, we express the problem in form of information bottleneck optimization, and we propose the agglomerative information bottleneck algorithm for finding a locally optimal solution. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions. |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik > Bioinspirierte Kommunikationssysteme 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik |
| Hinterlegungsdatum: | 07 Apr 2014 14:37 |
| Letzte Änderung: | 23 Sep 2021 14:31 |
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