Probabilistic Inference on the Maximum Entropy Principle

在Kullback和Leibler的意义上，最大熵原理被引入到一些感兴趣的陈述的未知确定性的估计中。为了从给定的相关陈述的确定性值中获得估计，从理论角度和实用的多功能性两个方面进行了讨论，提出了一个程序，可以总结如下：(1)在操纵确定性时应使用概率演算。(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同时发生的频率。(3)对于满足给定边际条件的当前知识，在测度中寻找最接近的分布时，应在结果之后引入未知概率。我们的最终目标是设计和实现一个新的专家系统，该系统以最大熵原理以形式化的方式承认不确定性。制作一个小型实验系统的原型已经完成，但目前的版本远非完全令人满意。还有许多事情有待解决。与概率推理密切相关的定量学习模型也形成了本研究的一个主题。任何先前的知识或工作假设都应根据经验适度修正。从最初的知识分布（通过与专家的访谈形成或建立在其他一些基础上）转变为完全经验的知识分布的过程是我们最关心的。对过程行为的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之间的定量关系提供了一个很好的模型。

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.