讲座题目：Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems

主讲人：夏思薇 (中国民用航空飞行学院)

讲座时间：2022.4.1（星期五）晚上19:30

讲座地点：线上

腾讯会议：378 595 710

讲座对象：全校师生

主要内容：

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical Lasso Estimator (SLS-GLE). The procedure uses the estimated precision matrix to describe the specific information on the conditional dependence pattern among predictors, and encourages both sparsity on the regression model and the graphical model. We introduce the Laplacian quadratic penalty adopting the graph information, and give detailed discussions on the advantages of using the precision matrix to construct the Laplacian matrix. Theoretical properties and numerical comparisons are presented to show that the proposed method improves both model interpretability and accuracy of estimation. We also apply this method to a financial problem and prove that the proposed procedure is successful in assets selection.

主讲人简介：

夏思薇：博士，2021年毕业于重庆大学，统计学博士学位，现任中国民航飞行学院风云策略三站高等数学教研室讲师，主要从事高维数据，变量选择，线性模型，多元线性模型方面研究。

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