Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
A Computational Study of Search Strategies for Mixed Integer Programming
INFORMS Journal on Computing
Optimal structure identification with greedy search
The Journal of Machine Learning Research
Characterization of essential graphs by means of the operation of legal merging of components
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - New trends in probabilistic graphical models
Probabilistic Conditional Independence Structures: With 42 Illustrations (Information Science and Statistics)
Learning Bayesian Networks
Structure learning of Bayesian networks using constraints
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
A geometric view on learning Bayesian network structures
International Journal of Approximate Reasoning
Efficient Structure Learning of Bayesian Networks using Constraints
The Journal of Machine Learning Research
Operations Research Letters
Characteristic imsets for learning Bayesian network structure
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
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The basic idea of the geometric approach to learning a Bayesian network (BN) structure is to represent every BN structure by a certain vector. If the vector representative is chosen properly, it allows one to re-formulate the task of finding the global maximum of a score over BN structures as an integer linear programming (ILP) problem. Such a suitable zero-one vector representative is the characteristic imset, introduced by Studeny, Hemmecke and Lindner in 2010, in the proceedings of the 5th PGM workshop. 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 a polyhedral description of the respective domain of the ILP problem, that is, by means of a set of linear inequalities. This theoretical result opens the way to the application of ILP software packages. The advantage of our 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. We also describe some computational experiments based on this idea.