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# Learning Bounded Tree-width Bayesian Networks using Integer Linear Programming

*Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics*, PMLR 33:751-759, 2014.

#### Abstract

In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NP-hard in general but becomes tractable when the network has low tree-width. Since the inference problem is common in many application areas, we provide a practical algorithm for learning bounded tree-width Bayesian networks. We cast this problem as an integer linear program (ILP). The program can be solved by an anytime algorithm which provides upper bounds to assess the quality of the found solutions. A key component of our program is a novel integer linear formulation for bounding tree-width of a graph. Our tests clearly indicate that our approach works in practice, as our implementation was able to find an optimal or nearly optimal network for most of the data sets.