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Probabilistic Inference on the Maximum Entropy Principle

Research Project

Project/Area Number 06680292
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionScience University of Tokyo

Principal Investigator

NIKI Naoto  Science University of Tokyo, Dpt. Manag. Sci., Professor, 工学部, 教授 (10000209)

Co-Investigator(Kenkyū-buntansha) HASHIGUCHI Hiroki  Science University of Tokyo, Dpt. Manag. Sci., Research Associate, 工学部, 助手 (50266920)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1994: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsUncertainty / Kullback-Leibler Information / Subjective Probability / Maximum Entropy Principle / Leaning Process / Kullabck-Leibler情報量
Research Abstract

The maximum entropy principle is introduced in the sense of Kullback and Leibler into the estimation of unknown degrees of certainty on some statements of interest. For obtaining the estimates from the given certainty values of related statements, a procedure is proposed after discussions both from theoretical perspectives and from pragmatic versatility which can be summarized below : (1) Probability calculus should be used in manipulating certainties. (2) Knowledge about the statements should be stored in the form of discrete distribution about how often the events that those statements turn out to be true or false happen together. (3) Entailment of unknown probabilities should follow the results in finding the nearest distribution in the measure to the current knowledge that satisfies the given marginal conditions.
Our final goal lies in designing and implementing a new expert system that acknowledge uncertauinty in a formal manner on the maximum entropy principle. Prototyping for making a small experimental system has been done, but the current version is far from complete satisfaction. There are many things and matters remained to be fixed.
Closely related to the probabilistic inference, a quantitative learning model has also formed a subject of this research. Any prior knowledge or working hypothesis should be moderately modified with experience. Processes of transition from the initial knowledge distribution given by revelation, formed through interview with an expert or founded upon some other grounds, into the fully empirical one are of prime concern to us. Theoretical analysis and computer simulation study on the behavior of the processes show that it provides a good model for human understanding and memory on the quantitative relations among events.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (7 results)

All Other

All Publications (7 results)

  • [Publications] Hashiguchi H.and Niki N.: "Kostaka numbers and their roles in statistics." Proc.Fifth Japan-China Symp.Statist.90-93 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Niki N.,Nakagawa S.and Hashiguchi,H: "Computer algebra application to the distribution theory of multivariate statistics." Proc.1st Asian Tech.Conf.Math.689-696 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hashiguchi, H.and Niki N.: "Kostaka numbers and their roles in statistics." Proc. Fifth Japan-China Symp. Statist.90-93 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Niki N., Nakagawa S.and Hashiguchi, H.: "Computer algebra application to the distribution theory of multivariate statistics." Proc. 1st Asian Tech. Conf. Math.689-696 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Niki., Nakagawa S. and Hashiguchi, H.: "Computer algebra application to the distribution theory of multivariate statistics." Proc. 1st Asian Tech. Conf. Math.,. 689-696 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hashiguchi,H.& Niki,N.: "Kostaka Numbers and Their Roles in Statistics." Proc.Fifth Japan-China Symp.Statist.90-93 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 橋口博樹,仁木直人: "ヤングタブロ-の数え上げについて" 数式処理. 3(発表予定).

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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