L-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains

Takeharu Shiraga, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

Markov chain Monte Carlo (MCMC) is a standard technique to sample from a target distribution by simulating Markov chains. In an analogous fashion to MCMC, this paper proposes a deterministic sampling algorithm based on deterministic random walk, such as the rotor-router model (a.k.a. Propp machine). For the algorithm, we give an upper bound of the point-wise distance (i.e., infinity norm) between the "distributions" of a deterministic random walk and its corresponding Markov chain in terms of the mixing time of the Markov chain. As a result, for uniform sampling of #P-complete problems, such as 0-1 knapsack solutions, linear extensions, matchings, etc., for which rapidly mixing chains are known, our deterministic algorithm provides samples with a "distribution" with a point-wise distance at most ε from the target distribution, in time polynomial in the input size and ε-1.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings
PublisherSpringer Verlag
Pages25-36
Number of pages12
ISBN (Print)9783319087825
DOIs
Publication statusPublished - Jan 1 2014
Event20th International Computing and Combinatorics Conference, COCOON 2014 - Atlanta, GA, United States
Duration: Aug 4 2014Aug 6 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8591 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Computing and Combinatorics Conference, COCOON 2014
CountryUnited States
CityAtlanta, GA
Period8/4/148/6/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'L<sub>∞</sub>-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains'. Together they form a unique fingerprint.

  • Cite this

    Shiraga, T., Yamauchi, Y., Kijima, S., & Yamashita, M. (2014). L-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains. In Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings (pp. 25-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8591 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-08783-2_3