Chain graph structure learning based on minimal c-separation trees

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. Experimental studies under various settings demonstrate 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.