Bayesian方法的计算学习机制和问题求解

Computational learning mechanism of Bayesian approach and problem solving

从信息熵的角度讨论了无信息先验分布的Bayesian假设的合理性 ,着重分析了贝叶斯方法的计算学习机制 ,得出贝叶斯定理是将先验分布中的期望值与样本均值按各自的精度进行加权平均 ,精度越高者其权值越大 ,合理地综合了先验信息和后验信息。在共轭先验分布的前提下 ,可以将后验信息作为新的一轮计算的先验 ,用 Bayesian定理与进一步得到的样本信息进行综合。多次重复这个过程后 ,样本信息的影响越来越显著。因此 ,合理正确地指派先验分布对提高学习的效率和质量有重要意义。 Bayesian方法既可避免只使用先验信息可能带来的主观偏见 ,和缺乏样本信息时的大量盲目搜索 ,也可避免只使用后验信息带来的噪音的影响。因此 ,适用于具有概率统计特征的数据采掘和知识发现问题 ,尤其是样本难得或代价昂贵的问题。

This paper discusses the rationality of the Bayesian hypothesis of non informational prior from the information entropy point of view, and emphasizes the analysis of the computational learning mechanism in the Bayesian approach. The results show that the Bayesian theorem averages the expectation of priors and the means of samples weighted according to their precision, and the higher the precision is the bigger the corresponding weights are. With the premise of conjugate priors, the posterior can be used as the prior in successive combinations with new samples using the Bayesian theorem. When this procedure is repeated, the impact of samples is more and more important, so the assessment of priors is vital to the efficiency and quality of learning. The Bayesian approach is suitable for data mining and knowledge discovery problems characterized by probability and statistics.