学术报告

题      目：Robust Fused Lasso Penalized Huber Regression with Nonasymptotic Property and Implementation Studies

报  告  人：肖运海   教授  (邀请人：陈艳男 )

                                 河南大学

时      间：2022-10-21 16:00-17:00

腾 讯 会 议：900 699 798

报告人简介:

       肖运海，男，河南濮阳人，河南大学数学与统计学院教授、河南省特聘教授、博士生导师。研究方向为最优化算法及其应用。2007年7月博士毕业于湖南大学。主持国家自然科学基金3项，参加973计划1项。在优化领域权威期刊Math. Prog. Comput.、Comput. Optim. Appl.等发表学术论文40余篇。担任中国运筹学会副秘书长，中国工业与应用数学学会理事，河南省运筹学会副理事长、河南省应用数学中心执行主任、河南大学学术委员会委员等。

摘      要：

       For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't seem appropriate anymore. On the other hand, in high-dimensional statistics, some datasets are easily contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address both issues, in this talk, we propose an adaptive Huber regression for robust estimation and inference, in which, the fused lasso penalty is used to encourage the sparsity of the coefficients as well as the sparsity of their differences, i.e., local constancy of the coefficient profile. Theoretically, we establish its nonasymptotic estimation error bounds under ℓ2-norm in high-dimensional setting. The proposed estimation method is formulated as a convex, nonsmooth and separable optimization problem, hence, the alternating direction method of multipliers can be employed. In the end, we perform on simulation studies and real cancer data studies, which illustrate that the proposed estimation method is more robust and predictive.