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Optimal Kullback-Leibler Aggregation via Information Bottleneck

Geiger, B. C. and Petrov, T. and Kubin, G. and Koeppl, H. (2014):
Optimal Kullback-Leibler Aggregation via Information Bottleneck.
In: IEEE Transactions on Automatic Control, IEEE, ISSN 0018-9286,
[Online-Edition: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6...],
[Article]

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.

Item Type: Article
Erschienen: 2014
Creators: Geiger, B. C. and Petrov, T. and Kubin, G. and Koeppl, H.
Title: Optimal Kullback-Leibler Aggregation via Information Bottleneck
Language: English
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.

Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 07 Apr 2014 14:37
Official URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6...
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