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On Approximating the Stationary Distribution of Time-Reversible Markov Chains

  • Marco BressanEmail author
  • Enoch Peserico
  • Luca Pretto
Article
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Part of the following topical collections:
  1. Special Issue on Theoretical Aspects of Computer Science (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 π(v) of a state v in a chain with mixing time τ, 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 π(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-π(v) barrier”.

Keywords

Markov chains MCMC sampling Large graph algorithms Randomized algorithms Sublinear algorithms 

Notes

Acknowledgements

Marco Bressan is supported in part by the ERC Starting Grant DMAP 680153, by a Google Focused Research Award, and by the “Dipartimenti di Eccellenza 2018-2022” grant awarded to the Dipartimento di Informatica at Sapienza. Enoch Peserico is supported in part by Università degli Studi di Padova under Project CAEPAE.

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Authors and Affiliations

  1. 1.Dipartimento di InformaticaSapienza Università di RomaRomaItaly
  2. 2.Dipartimento di Ingegneria dell’InformazioneUniversità degli Studi di PadovaPadovaItaly

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