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2013 Fiscal Year Final Research Report

Mathematical foundation of efficient algorithms for statistical inference

Research Project

  • PDF
Project/Area Number 22300098
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

FUKUMIZU Kenji  統計数理研究所, 大学共同利用機関等の部局等, 教授 (60311362)

Co-Investigator(Kenkyū-buntansha) TANAKA Toshiyuki  京都大学, 情報学研究科, 教授 (10254153)
IKEDA Shiro  統計数理研究所, 数理・推論研究系, 准教授 (30336101)
KABASHIMA Yoshiyuki  東京工業大学, 総合理工学研究科, 教授 (80260652)
Project Period (FY) 2010-04-01 – 2014-03-31
Keywordsグラフ / アルゴリズム / 確率計算 / 情報幾何 / 位相幾何
Research Abstract

As a new mathematical method for analyzing propagation algorithms on graphs, a novel Graph zeta function has been proposed for the analysis of the loopy belief propagation algorithm, and used for revealing stronger theoretical results than the known ones. Also, a method of loop expansion has been proposed for analyzing the approximation error of the loopy belief propagation.
As a mathematical foundation of the expectation propagation, an infinite dimensional exponential family has been proposed based on positive definite kernels, and its estimation methods and theoretical properties have been studied.

  • Research Products

    (15 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (8 results) (of which Peer Reviewed: 7 results) Presentation (5 results) (of which Invited: 5 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Low-rank matrix reconstruction and clustering via approximate message passing2014

    • Author(s)
      R. Matsushita and T. Tanaka
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 26 Pages: 917-925

    • Peer Reviewed
  • [Journal Article] Kernel embeddings of conditional distributions2013

    • Author(s)
      L. Song, K. Fukumizu, and A. Gretton
    • Journal Title

      IEEE Signal Processing Magazine

      Volume: 30 Pages: 98-111

    • Peer Reviewed
  • [Journal Article] Kernel Bayes' Rule : Bayesian inference with positive definite kernels2013

    • Author(s)
      K. Fukumizu, L. Song, and A. Gretton
    • Journal Title

      Journal of Machine Learning Research

      Volume: 14 Pages: 3753-3783

    • Peer Reviewed
  • [Journal Article] Introduction to the issue on differential geometry in signal processing2013

    • Author(s)
      J. Manton, D. Applebaum, S. Ikeda, and N.I. Bihan
    • Journal Title

      IEEE Journal of Selected Topics in Signal Processing

      Volume: 7(4) Pages: 573-575

  • [Journal Article] Replica Plefka expansion of Ising systems2012

    • Author(s)
      M. Yasuda, Y. Kabashima, Y. and K. Tanaka
    • Journal Title

      Journal of Statistical Mechanics : Theory and Experiment

      Volume: P04002

    • Peer Reviewed
  • [Journal Article] Characteristic Kernels and RKHS Embedding of Measures2011

    • Author(s)
      B.K. Sriperumbudur, B.K., K. Fukumizu, and G.R.G. Lanckriet, G.R.G. Universality
    • Journal Title

      Journal of Machine Learning Research

      Volume: 12 Pages: 2389-2410

    • Peer Reviewed
  • [Journal Article] Graph Zeta function in the Bethe free energy in and loopy belief propagation2010

    • Author(s)
      Y. Watanabe and K. Fukumizu
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 22 Pages: 2017-2025

    • Peer Reviewed
  • [Journal Article] New graph polynomials form the Bethe approximation of the Ising Partition function2010

    • Author(s)
      Y. Watanabe and K. Fukumizu
    • Journal Title

      Combinatories, Probability and Computing

      Volume: 20 Pages: 299-320

    • Peer Reviewed
  • [Presentation] Regularization in kernel method for Bayesian inference2013

    • Author(s)
      K. Fukumizu
    • Organizer
      Applied Inverse Problem Conference
    • Year and Date
      20130700
    • Invited
  • [Presentation] Statistical Methods with Positive Definite Kernels2012

    • Author(s)
      K. Fukumizu
    • Organizer
      The 2nd IMS Asia-Pacific Rim Meeting
    • Year and Date
      20120700
    • Invited
  • [Presentation] Graph Zeta Function and Loopy Belief Propagation2011

    • Author(s)
      Watanabe, Y. and Fukumizu, K
    • Organizer
      2011 International Symposium on Nonlinear Theory and its Applications
    • Year and Date
      20110900
    • Invited
  • [Presentation] Statistical Inference with Reproducing Kernels2011

    • Author(s)
      K. Fukumizu
    • Organizer
      The 8th international ISAAC Congress
    • Year and Date
      20110800
    • Invited
  • [Presentation] Kernel Method for Bayesian Inference2010

    • Author(s)
      K. Fukumizu
    • Organizer
      The 2nd Asian Conference on Machine Learning
    • Year and Date
      20101100
    • Invited
  • [Book] カーネル法入門 -正定値カーネルによるデータ解析-2010

    • Author(s)
      福水健次
    • Publisher
      朝倉書店
  • [Remarks] ホームページ

    • URL

      http://www.ism.ac.jp/~fukumizu/

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Published: 2015-06-25   Modified: 2015-07-08  

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