Focused Generalized Method of Moments for Structural Learning in High-dimensional Causal Graphical Models

报告人：李长城
报告地点：数学与统计学院415报告厅
报告时间：2019年12月8日星期日
报告摘要：

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.

主讲人简介：
李长城，现为宾夕法尼亚州立大学统计系博士后，于北京大学数学学院获得学士学位，宾夕法尼亚州立大学获得统计学博士学位，主要研究方向为高维统计推断。