Optimal Kullback-Leibler aggregation via information bottleneck
Geiger, Bernhard
Petrov, Tatjana
Kubin, Gernot
Koeppl, Heinz
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.
IEEE
2015
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/1840
Geiger B, Petrov T, Kubin G, Koeppl H. Optimal Kullback-Leibler aggregation via information bottleneck. <i>IEEE Transactions on Automatic Control</i>. 2015;60(4):1010-1022. doi:<a href="https://doi.org/10.1109/TAC.2014.2364971">10.1109/TAC.2014.2364971</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2014.2364971
info:eu-repo/semantics/altIdentifier/issn/0018-9286
info:eu-repo/semantics/openAccess