Directed Adaptive Graphical Lasso for causality inference

Graphical lasso provides a general solution to reveal the indirect statistic dependence of multiple variables in the high dimensional space. Rather than the undirected relationships, a number of practical problems concern much about the causality between nodes in terms of directed links. To address this challenge, in this letter, we propose Directed Adaptive Graphical Lasso (DAGL), a general framework for directed graph structure inference in the framework of sparse learning and graph theory. Both the experiments from simulation and cellular signaling system identification verify that DAGL could robustly predict the directed graph structure and accurately reveal the inherent causality between nodes.