Information theoretic study of empirical probability

• Project/Area Number: 22654015
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: FUJIWARA Akio 大阪大学, 理学研究科, 教授 (30251359)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 統計数学 / 経験確率 / 情報理論 / ユニバーサル符号化 / ランダムネス / ダイバージェンス

Research Abstract

We explored an information theoretic study of empirical probability. The main results are summarized as follows: 1) A novel Martin-Loef randomness criterion for two distinct computable probability measures was obtained based on finite-type quasi-symmetric divergence functions. 2) An alternative proof of a game-theoretic law of large numbers was given based on the Lynch-Davisson universal coding algorithm, and a possibility of generalizing the law of large numbers and the theorem of convergence of opinions to a general prediction game was pointed out.

Research Products

• [Presentation] Convex games, randomness, and geometry (2013)
  • Author(s): 藤原彰夫
  • Organizer: 研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
  • Place of Presentation: 大阪大学
  • Year and Date: 2013-03-14
• [Presentation] Convex games, randomness, and geometry (2013)
  • Author(s): 藤原彰夫
  • Organizer: 研究集会「エルゴード理論，情報理論，計算機科学とその周辺」
  • Place of Presentation: 大阪大学
• [Presentation] Randomness criteria in terms of f-divergences (2011)
  • Author(s): 藤原彰夫
  • Organizer: 研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2011-03-05
• [Presentation] Randomness criteria in terms of f-divergences (2011)
  • Author(s): 藤原彰夫
  • Organizer: 研究集会「エルゴード理論,情報理論,計算機科学とその周辺」
  • Place of Presentation: 統計数理研究所(東京都)(招待講演)
  • Year and Date: 2011-03-05
• [Presentation] Randomness criteria in terms of f-divergences (2010)
  • Author(s): Akio Fujiwara
  • Organizer: Third workshop on game theoretic probability and related topics
  • Place of Presentation: Royal Holloway, University of London
  • Year and Date: 2010-06-23
• [Presentation] Randomness criteria in terms of f-divergences (2010)
  • Author(s): 藤原彰夫
  • Organizer: Third Workshop on Game-Theoretic Probability and Related Topics
  • Place of Presentation: Royal Holloway, University of London (UK)(招待講演)
  • Year and Date: 2010-06-23
• [Remarks]
  • URL: http://www.math.sci.osaka-u.ac.jp/~fujiwara