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