Learning Bayesian Network Structure using LP Relaxations. Jaakkola, T., Sontag, D., Globerson, A., & Meila, M. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AI-STATS), volume 9, pages 358-365, 2010. JMLR: W&CP.
Learning Bayesian Network Structure using LP Relaxations [pdf]Paper  abstract   bibtex   
We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty arises from the global constraint that the graph structure has to be acyclic. We cast the structure learning problem as a linear program over the polytope defined by valid acyclic structures. In relaxing this problem, we maintain an outer bound approximation to the polytope and iteratively tighten it by searching over a new class of valid constraints. If an integral solution is found, it is guaranteed to be the optimal Bayesian network. When the relaxation is not tight, the fast dual algorithms we develop remain useful in combination with a branch and bound method. Empirical results suggest that the method is competitive or faster than alternative exact methods based on dynamic programming.
@inproceedings{JaaSonGloMei_aistats10,
 title  = {Learning {B}ayesian Network Structure using {LP} Relaxations},
 author = {Tommi Jaakkola and David Sontag and Amir Globerson and Marina Meila},
 booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AI-STATS)},
 publisher = {JMLR: W\&CP},
 volume = {9},
 pages  = {358-365},
 year = {2010},
 keywords = {Machine learning, Bayesian network structure learning},
 url_Paper = {http://people.csail.mit.edu/dsontag/papers/structure_aistats10.pdf},
 abstract = {We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty arises from the global constraint that the graph structure has to be acyclic. We cast the structure learning problem as a linear program over the polytope defined by valid acyclic structures. In relaxing this problem, we maintain an outer bound approximation to the polytope and iteratively tighten it by searching over a new class of valid constraints. If an integral solution is found, it is guaranteed to be the optimal Bayesian network. When the relaxation is not tight, the fast dual algorithms we develop remain useful in combination with a branch and bound method. Empirical results suggest that the method is competitive or faster than alternative exact methods based on dynamic programming.}
}
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