Advances in Learning Bayesian Networks of Bounded Treewidth

TL;DR

This paper introduces new algorithms for learning Bayesian network structures with bounded treewidth, combining exact mixed-integer programming and approximate sampling methods, and demonstrates their superior performance on real datasets.

Contribution

It presents novel exact and approximate algorithms for learning bounded treewidth Bayesian networks, improving over existing methods in accuracy and efficiency.

Findings

Exact algorithm outperforms state-of-the-art methods.

Approximate approach achieves high accuracy.

Methods are empirically validated on datasets with up to 100 variables.

Abstract

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.