Fast Bayesian Network Structure Search Using Gaussian Processes

In this paper we introduce two novel methods for performing Bayesian network structure search that make use of Gaussian Process regression. Using a relatively small number of samples from the posterior distribution of Bayesian networks, we are able to find an accurate function approximator based on Gaussian Processes. This allows us to remove our dependency on the data during the search and leads to massive speed improvements without sacrificing performance. We use our function approximator in the context of Hill Climbing, a local-score based search algorithm, and in the context of a global optimization technique based on response surfaces. We applied our methods to both synthetic and real data. Results show that we converge to networks of equal score to those found by traditional Hill Climbing, but at a fraction of the total time.