Reviews: Globally optimal score-based learning of directed acyclic graphs in high-dimensions

Update: The authors gave a good rebuttal, I have increased my score to 6. Original comments: In this paper, the authors considered the problem of learning directed acyclic graphs via optimizing a score. In particular, they have developed a new approach that requires O(s log p) samples to learn a DAG from the data. The proposed a approach is an optimization based approach that learns a DAG via optimizing a nonconvex scoring function. The theoretical analysis of this paper is complete. In addition, the analysis techniques developed in this paper seems to be helpful to solve other related problems in structure learning and high-dimensional statistics.