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A Tuning-free Robust and Efficient Approach to High-dimensional Regression
时间:2020年10月16日 11:29 点击数:

报告人:李润泽

报告地点:腾讯会议

报告时间:2020年10月17日星期六10:00-11:00

邀请人:郑术蓉

报告摘要:

We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintaining high efficiency for normal random errors. Comparing with other alternative robust regression procedures, it also enjoys the property of being equivariant when the response variable undergoes a scale transformation. Computationally, it can be efficiently solved via linear programming. Theoretically, under weak conditions on the random error distribution, we establish a finite-sample error bound with a near-oracle rate for the new estimator with the simulated tuning parameter. Our results make useful contributions to mending the gap between the practice and theory of Lasso and its variants. We also prove that further improvement in efficiency can be achieved by a second-stage enhancement with some light tuning. Our simulation results demonstrate that the proposed methods often outperform cross-validated Lasso in various settings.

会议ID:205 540 189

主讲人简介:

李润泽是宾州州立大学统计冠名讲习教授。他曾担任国际顶级学术期刊统计年刊的主编,副主编。自2006年起,他一直担任另一个统计学顶级学术期刊美国统计协会杂志副主编。他的研究方向包括高维数据建模,变量筛选,非参数统计推断,半参数统计推断及其统计学的应用。他已经发表了200多篇文章。自2014年以来,每年入选世界高被引科学家。他获得了许多荣誉,包括IMS fellow, ASA Fellow, AAAS fellow. ICSA 杰出成就奖。

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