---
_id: '1840'
abstract:
- lang: eng
  text: 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.
acknowledgement: "This work was supported by the Austrian Research Association under
  Project 06/12684, by the Swiss National Science Foundation (SNSF) under Grant PP00P2
  128503/1, by the SystemsX.ch (the Swiss Inititative for Systems Biology), and by
  a SNSF Early Postdoc.Mobility Fellowship grant P2EZP2_148797.\r\n"
author:
- first_name: Bernhard
  full_name: Geiger, Bernhard
  last_name: Geiger
- first_name: Tatjana
  full_name: Petrov, Tatjana
  id: 3D5811FC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrov
  orcid: 0000-0002-9041-0905
- first_name: Gernot
  full_name: Kubin, Gernot
  last_name: Kubin
- first_name: Heinz
  full_name: Koeppl, Heinz
  last_name: Koeppl
citation:
  ama: 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>
  apa: 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>
  chicago: 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>.
  ieee: 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.
  ista: 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.
  mla: 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>.
  short: B. Geiger, T. Petrov, G. Kubin, H. Koeppl, IEEE Transactions on Automatic
    Control 60 (2015) 1010–1022.
date_created: 2018-12-11T11:54:18Z
date_published: 2015-04-01T00:00:00Z
date_updated: 2021-01-12T06:53:33Z
day: '01'
department:
- _id: CaGu
- _id: ToHe
doi: 10.1109/TAC.2014.2364971
intvolume: '        60'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1304.6603
month: '04'
oa: 1
oa_version: Preprint
page: 1010 - 1022
publication: IEEE Transactions on Automatic Control
publication_identifier:
  issn:
  - 0018-9286
publication_status: published
publisher: IEEE
publist_id: '5262'
quality_controlled: '1'
scopus_import: 1
status: public
title: Optimal Kullback-Leibler aggregation via information bottleneck
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 60
year: '2015'
...