Structure learning in Bayesian networks and session analysis of people search within a professional social network

We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n − 1) potential edges in O(n2n) total time, assuming that the in-degree, i.e., the number of parents per node, is bounded by a constant. One main drawback of their algorithms is the requirement of a special structure prior that is non uniform and does not respect Markov equivalence. In this paper, we develop an algorithm that can compute the exact posterior probability of a subnetwork in O(3n) time and the posterior probabilities for all n(n− 1) potential edges in O(n3n) total time. Our algorithm also assumes a bounded in-degree but allows general structure priors. We demonstrate the applicability of the algorithm on several data sets with up to 20 variables.