学术报告

Estimation of Linear Functionals in High Dimensional Linear Models:From Sparsity to Non-sparsity- 赵俊龙 教授(北京师范大学统计学院教授)

报告题目:Estimation of Linear Functionals in High Dimensional Linear Models:From Sparsity to Non-sparsity

报告人: 赵俊龙 教授(北京师范大学统计学院教授)

摘要:High dimensional linear models are commonly used in practice. In many applications,  one is interested in linear transformations $\bbeta^\top x$ of regression coefficients $\bbeta\in \mR^p$, where $x$ is a specific point and is not required to be identically distributed as the training data. One common approach is the plug-in technique which first  estimates $\bbeta$, then plugs the estimator in the linear transformation for prediction. Despite its popularity, estimation of $\bbeta$ can be difficult for high dimensional problems. Commonly used  assumptions  in  the literature   include that the signal of coefficients $\bbeta$ is sparse and predictors are weakly correlated.   These  assumptions, however,  may not be easily verified, and can be violated in practice.When  $\bbeta$ is non-sparse or predictors are strongly correlated, estimation of $\bbeta$  can be  very difficult. In this paper, we  propose a novel pointwise estimator for linear transformations of $\bbeta$. This new estimator greatly relaxes the common assumptions for high dimensional problems, and is adaptive to the degree of  sparsity of $\bbeta$ and strength of correlations among the predictors. In particular,$\bbeta$ can be sparse or  non-sparse and predictors can be strongly or weakly correlated.The proposed method is simple for implementation.  Numerical  and theoretical results demonstrate the competitive advantages of  the proposed method for a wide range of problems.

报告人简介:赵俊龙,北京师范大学统计学院教授。 从事统计和机器学习相关研究,包括:高维数据分析、统计机器学习、稳健统计等。 在统计学顶级期刊Journal of the Royal Statistical Society: Series B(JRSSB)、 The Annals of Statistic(AOS)、Journal of American Statistical Association(JASA),Biometrika以及其他统计学重要期刊发了论文四十余篇。主持多项国家自然科学基金项目,参与国家自然科学基金重点项目。

报告时间:2023年6月5日(周一)上午10:30-11:30

报告地点:校本部教二楼627教室

邀请人:胡涛