Learning Bounded Treewidth Bayesian Networks with Thousands of Variables

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. We propose a novel algorithm for this task, able to scale to large domains and large treewidths. Our novel approach consistently outperforms the state of the art on data sets with up to ten thousand variables

Advances in Learning Bayesian Networks of Bounded Treewidth

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.Comment: 23 pages, 2 figures, 3 table

Cutset Sampling for Bayesian Networks

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks

Efficient learning of Bayesian networks with bounded tree-width

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [24,29] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. Finding the best k-tree, however, is computationally intractable. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing an informative score function to characterize the quality of a k-tree. To further improve the quality of the k-trees, we propose a probabilistic hill climbing approach that locally refines the sampled k-trees. The proposed algorithm can efficiently learn a quality Bayesian network with tree-width at most k. Experimental results demonstrate that our approach is more computationally efficient than the exact methods with comparable accuracy, and outperforms most existing approximate methods