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

Fingerprint

Markov processes
Discrepancy
Polynomial time
Polynomials
Markov chain
Markov Chain Monte Carlo
Random walk
Mixing Time
Linear Extension
Target
Knapsack
Sampling
Deterministic Algorithm
Router
Rotor
Routers
Infinity
Upper bound
Norm
Rotors

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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

L-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains. / Shiraga, Takeharu; Yamauchi, Yukiko; Kijima, Shuji; Yamashita, Masafumi.

Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag, 2014. p. 25-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8591 LNCS).

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

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8591 LNCS, Springer Verlag, pp. 25-36, 20th International Computing and Combinatorics Conference, COCOON 2014, Atlanta, GA, United States, 8/4/14. https://doi.org/10.1007/978-3-319-08783-2_3
Shiraga T, Yamauchi Y, Kijima S, Yamashita M. L-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains. In Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag. 2014. p. 25-36. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-08783-2_3
Shiraga, Takeharu ; Yamauchi, Yukiko ; Kijima, Shuji ; Yamashita, Masafumi. / L-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains. Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag, 2014. pp. 25-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{6d4773cbaedb4e9489761a03e5842f9b,
title = "L∞-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains",
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.",
author = "Takeharu Shiraga and Yukiko Yamauchi and Shuji Kijima and Masafumi Yamashita",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/978-3-319-08783-2_3",
language = "English",
isbn = "9783319087825",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "25--36",
booktitle = "Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings",
address = "Germany",

}

TY - GEN

T1 - L∞-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains

AU - Shiraga, Takeharu

AU - Yamauchi, Yukiko

AU - Kijima, Shuji

AU - Yamashita, Masafumi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84904756566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904756566&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-08783-2_3

DO - 10.1007/978-3-319-08783-2_3

M3 - Conference contribution

AN - SCOPUS:84904756566

SN - 9783319087825

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 25

EP - 36

BT - Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings

PB - Springer Verlag

ER -