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DOI: 10.4230/LIPIcs.STACS.2018.18
On Approximating the Stationary Distribution of Time-reversible Markov Chains

Authors: Marco Bressan, Enoch Peserico, and Luca Pretto

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
Approximating the stationary probability of a state in a Markov chain through Markov chain Monte Carlo techniques is, in general, inefficient. Standard random walk approaches require tilde{O}(tau/pi(v)) operations to approximate the probability pi(v) of a state v in a chain with mixing time tau, and even the best available techniques still have complexity tilde{O}(tau^1.5 / pi(v)^0.5); and since these complexities depend inversely on pi(v), they can grow beyond any bound in the size of the chain or in its mixing time. In this paper we show that, for time-reversible Markov chains, there exists a simple randomized approximation algorithm that breaks this "small-pi(v) barrier".
Cite as

Marco Bressan, Enoch Peserico, and Luca Pretto. On Approximating the Stationary Distribution of Time-reversible Markov Chains. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bressan_et_al:LIPIcs.STACS.2018.18,
  author =	{Bressan, Marco and Peserico, Enoch and Pretto, Luca},
  title =	{{On Approximating the Stationary Distribution of Time-reversible Markov Chains}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.18},
  URN =		{urn:nbn:de:0030-drops-84949},
  doi =		{10.4230/LIPIcs.STACS.2018.18},
  annote =	{Keywords: Markov chains, MCMC sampling, large graph algorithms, randomized algorithms, sublinear algorithms}
}
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