贝叶斯网络诱导的内积空间

Inner Product Spaces for Bayesian Networks

概率模型和核函数相结合的方法是学习系统的热点研究领域,贝叶斯网络是重要的一类概率图形模型。文中主要讨论了变量取值在布尔域上的两类分类任务,重点讨论了几个常见贝叶斯网络诱导的内积空间的最低维数,为解决一些常见的分类问题提供了理论依据。文中通过分析概念类的VC维来确定其欧几里德维数的下界,VC维还可用于估计贝叶斯网络概念类的复杂性和判断概念类的分类性能。

There has been a remarkable interest in learning systems that combine the key advantages of probabilistic models and kernel functions. Bayesian networks are one of the major probabilistic graphical models. We focus on two-label classification tasks over the Boolean domain. Emphasis is put on the lowest dimension of inner product spaces induced by several common cases of Bayesian networks, which serves as a theoretical foundation for the solution of common problems. The lower bounds are obtained by analyzing the VC dimension of the concept class associated with the Bayesian network. VC dimension can also be used to estimate the complexity of the concept class induced by Bayesian networks and judge the performance of the classification of the concept class.