【作者】 王鹏；

【导师】 欧阳丹彤；

【作者基本信息】 吉林大学 ， 计算机软件与理论， 2006， 硕士

【摘要】 Bayesian网作为一种不确定性信息处理的基于模型方法,是人工智能领域一个非常活跃的研究方向,并在各个领域逐步取得广泛应用。本文首先介绍了Bayesian网的一般概念及推理任务,并主要着眼于Bayesian网推理算法的数学原理,提出了样本平均值算法,对几种推理算法从数学角度做出本质性的刻画,给出各自的复杂度和精确度的理论分析,证明了他们在各种情况下的推理效率。提出了样本平均值算法,并实现了四个算法。通过实验测试了四种算法在各种情况下的推理时间。接下来介绍了Bayesian推理在图像分类器的设计中的应用。主要是在图像特征提取之后,如何用Bayesian推理的方法构造和设计分类器。最后介绍一个基于决策树的分类器测试平台,其中包括该系统的需求分析、模块结构以及各模块解决方法。平台作为分类器设计的辅助工具,为解决分类器设计开发中遇到的问题提供了有力的工具。更多还原

【Abstract】 Uncertain information processing is an important research area in Artificial intelligence. All the processing approaches fall into two categories - rule-based and model-based ones. Bayesian network was developed in 1980’s and has been paid increasing attention to since 1990’s. Compared with the early rule-based approaches, it has more clear semantics and usually makes more reasonable conclusions, but involves much more calculation.Inference in general Bayesian networks is NP hard. So far tens of Inference algorithms have been developed to make Bayesian networks as practical as possible. All the algorithms fall into two categories- exact ones and approximate ones. One early exact algorithm is variable elimination algorithm. One early approximate algorithm one is logic sampling algorithm. The basic idea of logic sampling is to stimulate the event that the Bayesian networks created. The inference result is the proportion of the amount of the samples, in which query event happened and the amount of all samples. This algorithm laid the foundations of other sampling inference algorithms, such as importance sampling algorithm and like-hood weight sampling algorithm.In this paper, the description of accurate and complexities of some kinds of sampling algorithms are presented on the basis of introduction to basic concepts of Bayesian networks. First, the mathematical foundations of them are given here in view of statistics. Second, the algorithms as well as the implements are given in detail in view of programming. Last, the complexity and accuracy analysis of each algorithm was presented.In probability logic sampling algorithm, all random events were simulated a large number of times. The inference result is the rate of samples, in which query event happened. The accuracy would increase along with the increase of the samples amount. Any two samples were independent. One sample would be discarded, if the sample was not coincident with this evidence node. So the complexity of the algorithm is O(N·M·2K), N is the amount of nodes, M is the amount of samples, K is the amount of evidences.At the following part, a new inference algorithm, samples-mean algorithm, was presented. The principle of this algorithm is an integral method extension from continuous unitary variable to discrete multivariable. We can get one entire sample by combining non-evidence-and-non-query nodes’random sample with evidence nodes and query nodes. And then, we can get a large number of samples by repeating such a process. The inference更多还原