Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into classes that predict the kinds of probabilistic dependencies they participate in. Here we capture this form of prior knowledge in a hierarchical Bayesian framework, and exploit it to enable structure learning and type discovery from small datasets. Specifically, we present a nonparametric generative model for directed acyclic graphs as a prior for Bayes net structure learning. Our model assumes that variables come in one or more classes and that the prior probability of an edge existing between two variables is a function only of their classes. We derive an MCMC algorithm for simultaneous inference of the number of classes, the class assignments of variables, and the Bayes net structure over variables. For several realistic, sparse datasets, we show that the bias towards systematicity of connections provided by our model yields more accurate learned networks than a traditional, uniform prior approach, and that the classes found by our model are appropriate.

本文提出了一种基于贝叶斯网络结构学习的非参数生成模型，采用分层贝叶斯框架来捕捉变量之间的系统性关系，通过MCMC算法推导出变量的类别、贝叶斯网络结构和类别间的先验概率，实验证明该方法在小样本数据集中更准确。

结构学习的结构先验