Advances in Learning Bayesian Networks of Bounded Treewidth
This work addresses the challenge of efficient structure learning in probabilistic graphical models for applications requiring bounded treewidth, representing an incremental advance in the field.
The paper tackles the problem of learning Bayesian network structures with bounded treewidth by developing novel exact and approximate algorithms, and shows that the exact algorithm outperforms state-of-the-art methods on datasets with up to 100 variables.
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.