Study on replica extension of approximate probability calculation algorithms

2008 Fiscal Year Self-evaluation Report

• Project/Area Number: 18079006
• Research Category: Grant-in-Aid for Scientific Research on Priority Areas
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: KABASHIMA Yoshiyuki Tokyo Institute of Technology, 大学院・総合理工学研究科, 教授 (80260652)
• Project Period (FY): 2006 – 2009
• Keywords: レプリカ拡張 / レプリカ対称性 / 平均場近似 / 解析接続 / 複素零点評価 / レプリカ数

Research Abstract

大規模な確率分布に付随する計算困難を実際的に解決する手段として, 近年確率伝搬法を代表とする平均場近似やマルコフ連鎖モンテカルロ法が注目され, 情報通信やデータ解析の分野を中心に顕著な成果が得られている. その一方で, これらのアルゴリズムは対象となる分布の形状が複雑になると, その性能が急激に悪化することが経験的に明らかになってきた. 本研究では, この問題を解決するためにスピングラス研究の成果に基づき代表者である樺島が最近導入した「レプリカ拡張」のアイデアをさまざまな近似的確率計算アルゴリズムに適用し, その有効性と限界を明らかにする.

Research Products

• [Journal Article] On analyticity with respect to the replica number in random energy models I: an exact expression of the moment of the partition function (2009)
  • Author(s): Kenzo Ogure and Yoshiyuki Kabashima
  • Journal Title: J. Stat. Mech. Pages: 03010
  • Peer Reviewed
• [Journal Article] Complex replica zeros of ±J Ising spin glass at zero temperature (2009)
  • Author(s): Tomoyuki Obuchi, Yoshiyuki Kabashima and Hidetoshi Nishimori
  • Journal Title: J. Phys. A: Math. Theor. 42 Pages: 075004(27pp)
  • Peer Reviewed
• [Journal Article] Learning from correlated patterns by simple perceptrons (2009)
  • Author(s): Takashi Shinzato and Yoshiyuki Kabashima
  • Journal Title: J. Phys. A: Math. Theor. 42 Pages: 015005(12pp)
  • Peer Reviewed
• [Journal Article] Perceptron capacity revisited: classification ability for correlated patterns (2008)
  • Author(s): Takashi Shinzato and Yoshiyuki Kabashima
  • Journal Title: J. Phys. A: Math. Theor. 41 Pages: 324013(18pp)
  • Peer Reviewed
• [Journal Article] Statistical mechanical analysis of the linear vector channel in digital communication (2007)
  • Author(s): Koujin Takeda, Atsushi Hatabu and Yoshiyuki Kabashima
  • Journal Title: J. Phys. A: Math. Theor. 40 Pages: 14085-14098
  • Peer Reviewed
• [Presentation] Analyticity breaking and complex zeros with respect to the replica number in random energy models (2009)
  • Author(s): Y. Kabashima
  • Organizer: The Science of Complexity
  • Place of Presentation: Eilat, Israel
  • Year and Date: 2009-03-31
• [Presentation] Replica symmetry breaking and solution search in a power reduction precoding problem of wireless communication (2008)
  • Author(s): Y. Kabashima and N. Hayashi
  • Organizer: Unifying Concepts in Glassy Physics IV(UCGP2008)
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2008-11-27
• [Presentation] An Integral Formula for Large Rectangular Matrices and Its Application to Analysis of Linear Vector Channels (2008)
  • Author(s): Y. Kabashima
  • Organizer: PHYSCOMNET08
  • Place of Presentation: Berlin, Germany
  • Year and Date: 2008-04-04
• [Presentation] Statistical mechanical approach to CDMA communication - an offspring of research on perceptrons and associative memory- (2007)
  • Author(s): Y. Kabashima
  • Organizer: 14th International Conference on Neural Information Processing(ICONIP2007)
  • Place of Presentation: Kitakyushu, Japan
  • Year and Date: 2007-11-16
• [Presentation] Belief and survey propagations in perceptrons (2007)
  • Author(s): Y. Kabashima
  • Organizer: Common Concepts in Statistical Physics and Computer Science
  • Place of Presentation: Trieste, Italy
  • Year and Date: 2007-07-06