Chain Graph Structure Learning Based on Minimal C-separation Trees

Abstract

Chain graphs are a comprehensive class of graphical models that describe conditional independence information, encompassing both Markov networks and Bayesian networks as particular instances. In this paper, we propose a computationally feasible algorithm for the structural learning of chain graphs based on the idea of “dividing and conquering”, decomposing the learning problem into a set of minimal scale problems on its decomposed subgraphs. To this aim, we propose the concept of minimal c-separation trees in chain graphs and provide a mechanism to generate them, based on which we conduct structural learning using the divide and conquer technique. Simulations under a variety of settings reveals that the presented structural learning algorithm for chain graphs generally outperforms existing methods. The code of this work is available at https://github.com/luyaoTan/mtlc.