Representing local structure in Bayesian networks by Boolean functions

A number of studies on learning Bayesian networks have emphasized the importance of exploiting regularities in conditional probability distributions, i.e., local structure. In this paper, we encode local structures as linear combinations of Boolean functions. By using Lasso, we can simultaneously estimate the structure and parameters of the networks from limited data. We demonstrate that the method leads to improved performance in terms of structural correctness as well as prediction score even when the local structure in the underlying model is only implicit.