How matroids occur in the context of learning Bayesian network structure

Milan Studený
2015 Conference on Uncertainty in Artificial Intelligence  
It is shown that any connected matroid having a non-trivial cluster of BN variables as its ground set induces a facet-defining inequality for the polytope(s) used in the ILP approach to globally optimal BN structure learning. The result applies to well-known k-cluster inequalities, which play a crucial role in the ILP approach.
dblp:conf/uai/Studeny15 fatcat:fmqgjbniavb2nd4wi7kuhs6cv4