Efficient learning of Bayesian networks with bounded tree-width

Siqi Nie, Cassio Polpo de Campos, Qiang Ji

Abstract: Highlights • This work presents a novel method for BN structure learning with bounded tree-width. • The algorithm is based on a fast bijection between k -trees and the Dandelion codes. • The Distance Preferable Sampling is designed to effectively cover the space of k -trees. • The probabilistic hill climbing algorithm is used to obtain k -trees of high quality. • Extensive experiments indicate the efficiency and effectiveness of the proposed algorithm. Abstract 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. Previous article in issue Next article in issue