报告题目：Focused Generalized Method of Moments for Structural Learning in High-dimensional Causal Graphical Models
报 告 人：Li Changcheng 博士后，宾夕法尼亚州立大学
In this paper, we propose a new constraint-based causal structural learning algorithm for high-dimensional Gaussian linear causal graphical models. Existing constraint-based approaches like the PC algorithm remove edges between vertices by carrying conditional independence tests on all possible candidates of d-separation sets. This can be computationally expensive and have exponential worst-case complexity. To tackle these issues, we propose a regularized approach called Focused Generalized Method of Moments (FGMM) to identify d-separation sets between vertices in this paper. Regularized approaches have been used to identify Markov blankets in causal graphical models. However, Markov blankets contain spouses besides true neighbors, which also need to be removed by searching d-separation sets. Distinguished from existing regularized approaches, the FGMM approach utilizes the moment conditions to identify d-separation sets directly. Furthermore, we propose an iterative linear approximation algorithm to solve the optimization problem in the FGMM approach efficiently. We further propose skeleton and structural learning algorithms based on the FGMM method, and establish the consistency of the FGMM algorithm in high-dimensional settings. We further conduct Monte Carlo simulations on various benchmark networks and show advantages of the proposed FGMM algorithm both in accuracy and speed.