Using weak prior information on structures to learn Bayesian Networks

Most of the approaches developed in the literature to elicit the a-priori distribution on Directed Acyclic Graphs (DAGs) require a full specification of graphs. Nevertheless, expert’s prior knowledge about conditional independence relations may be weak, making the elicitation task troublesome. Moreover, the detailed specification of prior distributions for structural learning is NP-Hard, making the elicitation of large networks impractical. This is the case, for example, of gene expression analysis, in which a small degree of graph connectivity is a priori plausible and where substantial information may regard dozens against thousands of nodes. In this paper we propose an elicitation procedure for DAGs which exploits prior knowledge on network topology, and that is suited to large Bayesian Networks. Then, we develop a new quasi-Bayesian score function, the P-metric, to perform structural learning following a score-and-search approach.