**统计与管理学院2018年学术报告第38期****【主 题】**Markov Neighborhood Regression for High-Dimensional Inference**【报告人】 Faming Liang**教授Purdue University

**【时 间】**2018年07月10日（星期二）10:00-11:00**【地 点】**上海财经大学统计与管理学院大楼1208会议室【

**摘 要**】This talk introduces an innovative method for constructing confidence intervals and assessing p-values in high-dimensional linear and generalized linear models. The proposed method has successfully reduced the high-dimensional inference problem to a series of low-dimensional inference problems: For each regression coefficient \beta_i, the confidence interval and p-value can be obtained by regressing on a subset of variables selected according to the conditional independence relations between the corresponding variable X_i and other variables. On the Markov network formed by all the variables X_1,X_2,\ldots,X_p, the subset of variables included in the low-dimensional regression forms a Markov neighborhood of X_i and thus the proposed method is coined as Markov neighborhood regression. The proposed method is tested on high-dimensional linear, logistic and Cox regression. The numerical results indicate that the proposed method significantly outperforms the existing ones. Based on the Markov neighborhood regression, a method for learning causal structures for high-dimensional linear and generalized linear models is proposed and applied to the problems of identification of drug sensitive genes and cancer driver genes. The idea of using conditional independence relations for dimension reduction is general and potentially can be extended to other high-dimensional or big data problems as well.