Bibliography

(eng): Learning Bayesian network structure is the NP-hard task of finding a directed acyclic graph that best fits real data. Two integer vector encodings exist – family variable and characteristic imset – which model the solution space of BN structure. Each encoding yields a polytope, the family variable and characteristic imset polytopes respectively. It has been shown that learning BN structure using a decomposable and score equivalent scoring criteria (such as BIC) is equivalent to optimizing a linear function over either the family-variable or characteristic imset polytope. This monograph is primarily intended for readers already familiar with BN but not familiar with polyhedral approaches to learning BN. Thus, this monograph focuses on the family-variable and characteristic imset polytopes, their known faces and facets, and more importantly, deep connections between their faces and facets. Specifically that many of the faces of the family variable polytope are superfluous when learning BN structure. Sufficient background on Bayesian networks, graphs, and polytopes are provided. The currently known faces and facets of each polytope are described. Deep connections between many of the faces and facets of family-variable and characteristic polytope are then summarized from recent results. Lastly, a brief history and background on practical approaches to learning BN structure using integer linear programming over both polytopes is provided.