Cutset networks: A simple, tractable, and scalable approach for improving the accuracy of Chow-Liu trees

Abstract

In this paper, we present cutset networks, a new tractable probabilistic model for representing multi-dimensional discrete distributions. Cutset networks are rooted OR search trees, in which each OR node represents conditioning of a variable in the model, with tree Bayesian networks (Chow-Liu trees) at the leaves. From an inference point of view, cutset networks model the mechanics of Pearl's cutset conditioning algorithm, a popular exact inference method for probabilistic graphical models. We present efficient algorithms, which leverage and adopt vast amount of research on decision tree induction for learning cutset networks from data. We also present an expectation-maximization (EM) algorithm for learning mixtures of cutset networks. Our experiments on a wide variety of benchmark datasets clearly demonstrate that compared to approaches for learning other tractable models such as thin-junction trees, latent tree models, arithmetic circuits and sum-product networks, our approach is significantly more scalable, and provides similar or better accuracy. © 2014 Springer-Verlag.