A polynomial-time perfect sampler for the Q-ising with a vertex-independent noise

M. Yamamoto, S. Kijima, Y. Matsui

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

抄録

We present a polynomial-time perfect sampler for the Q-Ising with a vertex-independent noise. The Q-Ising, one of the generalized models of the Ising, arose in the context of Bayesian image restoration in statistical mechanics. We study the distribution of Q-Ising on a two-dimensional square lattice over n vertices, that is, we deal with a discrete state space {1,...,Q} n for a positive integer Q. Employing the Q-Ising (having a parameter β) as a prior distribution, and assuming a Gaussian noise (having another parameter α), a posterior is obtained from the Bayes' formula. Furthermore, we generalize it: the distribution of noise is not necessarily a Gaussian, but any vertex-independent noise. We first present a Gibbs sampler from our posterior, and also present a perfect sampler by defining a coupling via a monotone update function. Then, we show O(nlogn) mixing time of the Gibbs sampler for the generalized model under a condition that β is sufficiently small (whatever the distribution of noise is). In case of a Gaussian, we obtain another more natural condition for rapid mixing that α is sufficiently larger than β. Thereby, we show that the expected running time of our sampler is O(nlogn).

本文言語英語
ホスト出版物のタイトルComputing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
ページ328-337
ページ数10
DOI
出版ステータス出版済み - 2009
外部発表はい
イベント15th Annual International Conference on Computing and Combinatorics, COCOON 2009 - Niagara Falls, NY, 米国
継続期間: 7 13 20097 15 2009

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5609 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他15th Annual International Conference on Computing and Combinatorics, COCOON 2009
国/地域米国
CityNiagara Falls, NY
Period7/13/097/15/09

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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