Learning Bayesian Networks: A MAP Criterion for Joint Selection of Model Structure and Parameter
Learning Bayesian Networks: A MAP Criterion for Joint Selection of Model Structure and Parameter
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学习贝叶斯网络：模型结构和参数联合选择的 MAP 准则
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Riggelsen
中科院分区：
文献类型：
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作者：
C. Riggelsen
为了学习贝叶斯网络（BN）结构，使用贝叶斯狄利克雷（BD）评分标准已成为常见的做法。与功能上可以被解释为正则化最大似然准则的大多数其他评分度量相比，BD度量不能被认为是正则化最大似然准则。从分析的角度来看，BD度量与其他度量相比的功能不相似性是一个障碍;例如，这在用于从不完整数据学习BN的结构EM算法的上下文中变得清晰。此外，要精确地指出为什么以及在多大程度上通过应用BD度量来处理正则化并不容易。我们引入了一个贝叶斯评分标准，是密切相关的BD度量，但解决了BD度量的明显缺点。我们通过使用与BD度量相同的基本假设来得出这个结果，但与BD度量相反，BD度量的重点是只学习模型结构，我们的目标是联合学习最可能的BN对，即，模型结构和参数被选择为一对。这种方法产生一个评分度量，具有正则化的最大似然度量的函数形式。我们进行实验，并表明，这MAP BN度量也产生更好的结果比BIC和BD度量独立的测试数据。
For learning Bayesian Network (BN) structures, it has become common practice to use the Bayesian Dirichlet (BD) scoring criterion. In contrast to most other scoring metrics that functionally can be interpreted as regularized maximum likelihood criteria, the BD metric cannot be considered as such. The functional dissimilarity of the BD metric compared to other metrics is an obstacle from an analytical point of view; this is for instance becomes clear in the context of the structural EM algorithm for learning BNs from incomplete data. Also, it is not easy to pin-point why exactly and to what extend regularization is taken care of by applying the BD metric. We introduce a Bayesian scoring criterion that is closely related to the BD metric, but solves the obvious disadvantages of the BD metric. We arrive at this result by using the same basic assumptions as for the BD metric, but in contrast to the BD metric, where focus is on learning the model structure only, we aim at learning the most probable BN pair jointly, i.e., model structure and the parameter are selected as a pair. This approach yields a scoring metric that has the functional form of a regularized maximum likelihood metric. We perform experiments, and show that this MAP BN metric also yields better results than the BIC and BD metrics on independent test data.