Structured Priors for Structure Learning
This work addresses the challenge of structure learning in Bayesian networks for domains with systematic dependencies, offering an incremental improvement by enabling better performance with limited data.
The authors tackled the problem of learning Bayesian network structures from small datasets by introducing a hierarchical Bayesian framework that incorporates structured priors based on variable classes, resulting in more accurate learned networks compared to traditional uniform priors for several realistic, sparse datasets.
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.