GroupLiNGAM: Linear non-Gaussian acyclic models for sets of variables

Abstract: Finding the structure of a graphical model has been received much attention in many fields. Recently, it is reported that the non-Gaussianity of data enables us to identify the structure of a directed acyclic graph without any prior knowledge on the structure. In this paper, we propose a novel non-Gaussianity based algorithm for more general type of models; chain graphs. The algorithm finds an ordering of the disjoint subsets of variables by iteratively evaluating the independence between the variable subset and the residuals when the remaining variables are regressed on those. However, its computational cost grows exponentially according to the number of variables. Therefore, we further discuss an efficient approximate approach for applying the algorithm to large sized graphs. We illustrate the algorithm with artificial and real-world datasets.