article published yes Bernhard Geiger author Tatjana Petrov author 3D5811FC-F248-11E8-B48F-1D18A9856A870000-0002-9041-0905 Gernot Kubin author Heinz Koeppl author CaGu department ToHe department 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. IEEE2015 eng 0018-9286 1304.6603 00035173160000910.1109/TAC.2014.2364971 6041010 - 1022 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> B. Geiger, T. Petrov, G. Kubin, H. Koeppl, IEEE Transactions on Automatic Control 60 (2015) 1010–1022. B. Geiger, T. Petrov, G. Kubin, and H. Koeppl, “Optimal Kullback-Leibler aggregation via information bottleneck,” <i>IEEE Transactions on Automatic Control</i>, vol. 60, no. 4. IEEE, pp. 1010–1022, 2015. Geiger, B., Petrov, T., Kubin, G., &#38; Koeppl, H. (2015). Optimal Kullback-Leibler aggregation via information bottleneck. <i>IEEE Transactions on Automatic Control</i>. IEEE. <a href="https://doi.org/10.1109/TAC.2014.2364971">https://doi.org/10.1109/TAC.2014.2364971</a> Geiger B, Petrov T, Kubin G, Koeppl H. 2015. Optimal Kullback-Leibler aggregation via information bottleneck. IEEE Transactions on Automatic Control. 60(4), 1010–1022. Geiger, Bernhard, et al. “Optimal Kullback-Leibler Aggregation via Information Bottleneck.” <i>IEEE Transactions on Automatic Control</i>, vol. 60, no. 4, IEEE, 2015, pp. 1010–22, doi:<a href="https://doi.org/10.1109/TAC.2014.2364971">10.1109/TAC.2014.2364971</a>. Geiger, Bernhard, Tatjana Petrov, Gernot Kubin, and Heinz Koeppl. “Optimal Kullback-Leibler Aggregation via Information Bottleneck.” <i>IEEE Transactions on Automatic Control</i>. IEEE, 2015. <a href="https://doi.org/10.1109/TAC.2014.2364971">https://doi.org/10.1109/TAC.2014.2364971</a>. 18402018-12-11T11:54:18Z2025-09-23T09:45:33Z