R. Hemmecke, S.Lindner, M. Studeny: Characteristic imsets for learning Bayesian network structure. International Journal of Approximate Reasoning 53 (2012), n. 9, pp. 1336-1349.

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, Vomlel, Hemmecke 2010) 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.

AMS classification 68T30, 52B12, 62H05

learning Bayesian network structure
essential graph
standard imset
characteristic imset
LP relaxation of a polytope

A pdf version of the published paper (337kB) is already open-access available.

The paper builds on results from the following publications: