Probabilistic Inference on the Maximum Entropy Principle
Project/Area Number  06680292 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
Statistical science

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

CoInvestigator(Kenkyūbuntansha) 
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)

Keywords  Uncertainty / KullbackLeibler Information / Subjective Probability / Maximum Entropy Principle / Leaning Process / KullabckLeibler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
(3results)
Research Output
(7results)