Bibliography

(eng): The basic idea of a geometric approach to learning a Bayesian network (BN) structure is to represent every BN structure by a certain vector. This may allow one to re-formulate the task of finding the global maximum of a score over BN structures as an integer linear programming (ILP) problem. Suitable such a zero-one vector representative is the characteristic imset, introduced in 2010. In this paper, extensions of characteristic imsets are considered which additionally encode chain graphs without flags equivalent to acyclic directed graphs. The main contribution is the polyhedral description of the respective domain of the ILP problem. The advantage of this approach is that, as a by-product of the ILP optimization procedure, one may get the essential graph, which is a traditional graphical BN representative.