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Probabilistic Inference on the Maximum Entropy Principle

最大熵原理的概率推理

基本信息

批准号：
06680292
负责人：
NIKI Naoto
金额：
$ 1.28万
依托单位：
Science University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

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.

在Kullback和Leibler的意义下，最大熵原理被引入到一些感兴趣的陈述的未知确定度的估计中。从理论和语用的通用性两个方面讨论了如何从相关陈述的确定性值中获得估计值的问题，并提出了一种方法：（1）利用概率演算来处理估计值。(2)关于这些陈述的知识应该以离散分布的形式存储，即这些陈述被证明为真或假的事件一起发生的频率。(3)未知概率的蕴涵应遵循在满足给定的边际条件的当前知识的测量中找到最接近的分布的结果，我们的最终目标在于设计和实现一个新的专家系统，以形式化的方式承认不确定性的最大熵原则。一个小型实验系统的原型已经完成，但目前的版本还远远不能完全令人满意。与概率推理密切相关的定量学习模型也是本研究的一个主题。任何先前的知识或工作假设都应该根据经验进行适度的修改。我们主要关心的是，从最初的知识分布（通过与专家的访谈或基于其他理由形成）到完全经验的知识分布的过渡过程。理论分析和计算机模拟研究表明，它为人类理解和记忆事件间的数量关系提供了一个很好的模型。