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Polynomial time approximate or perfect samplers for discretized Dirichlet distribution

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Abstract

In this paper, we propose two Markov chains for sampling random vectors that are distributed according to discretized Dirichlet distribution. Their mixing rates are bounded by O(n 2 log Δ) and O(n 3 log Δ), where n is the dimension and 1/Δ is the grid size for discretization. Our second chain gives a perfect sampler that is based on monotone coupling from the past. We also report the results of simulations.

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Authors and Affiliations

  1. Department of Information and System Engineering, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Tomomi Matsui

  2. Department of Computer Engineering and International Communication, Kanazawa Technical College, 2-270 Hisayasu, Kanazawa, Ishikawa, 921-8601, Japan

    Mitsuo Motoki

  3. Institute of Rheumatology, Tokyo Women’s Medical University, 10-22 Kawada-cho, Shinjuku-ku, Tokyo, 162-0054, Japan

    Naoyuki Kamatani

  4. Department of Informatics, Graduate School of ISEE, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395, Japan

    Shuji Kijima

Authors
  1. Tomomi Matsui
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  2. Mitsuo Motoki
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  3. Naoyuki Kamatani
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  4. Shuji Kijima
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Corresponding author

Correspondence to Shuji Kijima.

Additional information

Some of the results on the approximate sampler described in this paper appeared without detailed discussions in the extended abstract [17] in the Proceedings of ISAAC 2003 (The 14th Annual International Symposium on Algorithms and Computation), and some of the results on the perfect sampler described in this paper appeared without computational experiences in the extended abstract [18] in the post conference book of The Grammar of Technology Development.

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Matsui, T., Motoki, M., Kamatani, N. et al. Polynomial time approximate or perfect samplers for discretized Dirichlet distribution. Japan J. Indust. Appl. Math. 27, 91–123 (2010). https://doi.org/10.1007/s13160-010-0002-0

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  • DOI: https://doi.org/10.1007/s13160-010-0002-0

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