Overlapping decomposition for causal graphical modeling

Causal graphical models are developed to detect the dependence relationships between random variables and provide intuitive explanations for the relationships in complex systems. Most of existing work focuses on learning a single graphical model for all the variables. However, a single graphical model cannot accurately characterize the complicated causal relationships for a relatively large graph. In this paper, we propose the problem of estimating an overlapping decomposition for Gaussian graphical models of a large scale to generate overlapping sub-graphical models. Specifically, we formulate an objective function for the overlapping decomposition problem and propose an approximate algorithm for it. A key theory of the algorithm is that the problem of solving a κ+1 node graphical model can be reduced to the problem of solving a one-step regularization based on a solved κ node graphical model. Based on this theory, a greedy expansion algorithm is proposed to generate the overlapping subgraphs. We evaluate the effectiveness of our model on both synthetic datasets and real traffic dataset, and the experimental results show the superiority of our method.