Total variation discrepancy of deterministic random walks for ergodic Markov chains

Takeharu Shiraga, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

2 引用 (Scopus)

抜粋

Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates deterministic random walks, which is a deterministic process analogous to a random walk. While there are some progress on the analysis of the vertex-wise discrepancy (i.e., L discrepancy), little is known about the total variation discrepancy (i.e., Li discrepancy), which plays a significant role in the analysis of an FPRAS based on MCMC. This paper investigates upper bounds of the L1 discrepancy between the expected number of tokens in a Markov chain and the number of tokens in its corresponding deterministic random walk. First, we give a simple but nontrivial upper bound O(mt∗) of the L1 discrepancy for any ergodic Markov chains, where m is the number of edges of the transition diagram and t∗ is the mixing time of the Markov chain. Then, we give a better upper bound O(m√t∗ log t∗) for non-oblivious deterministic random walks, if the corresponding Markov chain is ergodic and lazy. We also present some lower bounds.

元の言語英語
ホスト出版物のタイトル13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016
編集者James Allen Fill, Mark Daniel Ward
出版者Society for Industrial and Applied Mathematics Publications
ページ138-148
ページ数11
ISBN(電子版)9781510819696
DOI
出版物ステータス出版済み - 2016
イベント13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 - Arlington, 米国
継続期間: 1 11 2016 → …

出版物シリーズ

名前13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016

その他

その他13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016
米国
Arlington
期間1/11/16 → …

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Materials Chemistry
  • Discrete Mathematics and Combinatorics

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  • これを引用

    Shiraga, T., Yamauchi, Y., Kijima, S., & Yamashita, M. (2016). Total variation discrepancy of deterministic random walks for ergodic Markov chains. : J. A. Fill, & M. D. Ward (版), 13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 (pp. 138-148). (13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611974324.13