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

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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

T2 - 20th International Computing and Combinatorics Conference, COCOON 2014

Y2 - 4 August 2014 through 6 August 2014

ER -