License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.18
URN: urn:nbn:de:0030-drops-84949
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8494/
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Bressan, Marco ; Peserico, Enoch ; Pretto, Luca

On Approximating the Stationary Distribution of Time-reversible Markov Chains

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LIPIcs-STACS-2018-18.pdf (0.6 MB)

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".

BibTeX - Entry

@InProceedings{bressan_et_al:LIPIcs:2018:8494,
  author =	{Marco Bressan and Enoch Peserico and Luca Pretto},
  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 =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8494},
  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}
}

Keywords: Markov chains, MCMC sampling, large graph algorithms, randomized algorithms, sublinear algorithms
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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