New Local Move Operators for Bayesian Network Structure Learning

We propose new local move operators incorporated into a score-based stochastic greedy search algorithm to efficiently escape from local optima in the search space of directed acyclic graphs. We extend the classical set of arc addition, deletion, and reversal operators with a new operator replacing or swapping one parent to another for a given node, i.e. combining two elementary operations (arc addition and deletion) in one move. The operators are further extended by doing more operations in one move in order to overcome the acyclicity constraint of Bayesian networks. These extra operations are temporally performed in the space of directed cyclic graphs, acyclicity being restored at the end and the move kept if it increases the score. Our experimental results on standard Bayesian networks and challenging gene regulatory nets show large BDeu improvements compared to state-of-the-art structure learning algorithms when the sample size is small.