Characteristic imsets for learning Bayesian network structure

The motivation for the paper is the geometric approach to learning Bayesian network (BN) structure. The basic idea of our approach is to represent every BN structure by a certain uniquely determined vector so that usual scores for learning BN structure become affine functions of the vector representative. The original proposal from Studeny et al. (2010) [26] was to use a special vector having integers as components, called the standard imset, as the representative. In this paper we introduce a new unique vector representative, called the characteristic imset, obtained from the standard imset by an affine transformation. Characteristic imsets are (shown to be) zero-one vectors and have many elegant properties, suitable for intended application of linear/integer programming methods to learning BN structure. They are much closer to the graphical description; we describe a simple transition between the characteristic imset and the essential graph, known as a traditional unique graphical representative of the BN structure. In the end, we relate our proposal to other recent approaches which apply linear programming methods in probabilistic reasoning. (C) 2012 Elsevier Inc. All rights reserved.