四值贝叶斯网络诱导的内积空间

Inner product spaces induced by Bayesian networks with four values

结合贝叶斯网络与核函数,通过概率分布等价性的转换,分析了四值贝叶斯网络诱导的内积空间,得到无连接、全连接以及k个节点具有一个父节点的特殊四值贝叶斯网络诱导的内积空间的最低维数。为进一步研究多值贝叶斯网络诱导的内积空间开辟了新途径,还通过分析概念类的VC维确定了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。

Combining Bayesian networks and kernel functions,the inner product spaces induced by Bayesian network with four values is analyzed through the transform of probability distribution equivalence property.As main results,the smallest dimension for the inner product space induced by four-valued Bayesian network with the non-connection,full connection and one parent node in k nodes was obtained.The results provide a new method to study the inner product spaces induced by Bayesian networks with multiple-valued nodes.The lower bounds are obtained by analyzing the VC dimension of the concept class associated with the Bayesian network.VC dimension can be used to estimate the complexity of the concept class induced by Bayesian network and judge the classification performance of the concept class.