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| Title: | A rapidly mixing approximate sampler of Dirichlet distribution |
| Authors: | Natsui, T
Motoki, M
Kamatani, N |
| Issue Date: | 2003-03 |
| Publisher: | 情報処理学会 |
| Magazine name: | 情報処理学会研究報告 : アルゴリズム研究会報告 |
| Volume: | 2003 |
| Number: | 32 |
| Start page: | 33 |
| End page: | 40 |
| Abstract: | In this paper, we propose a Markov chain for sampling a random variable distributed according to a discretized Dirichlet distribution. We show that our Markov chain is rapidly mixing, that is, the mixing time of our chain is (1/2)n(n-1)1n((Δ－ｎ)ε＾＜－1＞) where n is the dimension (the number of parameters), 1/Δ is the grid size for discretization, and εis the error bound. We estimate the mixing time by using the path coupling method. When the parameters are large, the log-concavity of the density function implies the rapidity straight forwardly. In the case that parameters are small, the density function is convex and so we need a different approach to use the path coupling method. We also show the rate of convergence of our chain experimentally. |
| Rights: | 社団法人 情報処理学会, 松井知己／元木光雄／鎌谷直之, 情報処理学会研究報告 : アルゴリズム研究会報告, 2003(32), 2003, 33-40. ここに掲載した著作物の利用に関する注意: 本著作物の著作権は（社）情報処理学会に帰属します。本著作物は著作権者である情報処理学会の許可のもとに掲載するものです。ご利用に当たっては「著作権法」ならびに「情報処理学会倫理綱領」に従うことをお願いいたします。 The copyright of this material is retained by the Information Processing Society of Japan (IPSJ). This material is published on this web site with the agreement of the author (s) and the IPSJ. Please be complied with Copyright Law of Japan and the Code of Ethics of the IPSJ if any users wish to reproduce, make derivative work, distribute or make available to the public any part or whole thereof. All Rights Reserved, Copyright (C) Information Processing Society of Japan. |
| URI: | http://hdl.handle.net/10119/3309 |
| Material Type: | publisher |
| Appears in Collections: | f10-1. 雑誌掲載論文 (Journal Articles)
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