报告题目：Statistical Robustness of Kernel Learning Estimator with Respect to Data Perturbation

报 告 人：孙海琳 教授（南京师范大学）

报告时间：2026年4月27日（星期一）8:40—9:20

报告地点：6776永利集团114（小报告厅）      

校内联系人：张立卫 教授         联系方式：84708351-8320

报告摘要：Inspired by the recent work [30] on the statistical robustness of empirical risks in reproducing kernel Hilbert space (RKHS) where the training data are potentially perturbed or even corrupted, we take a step further in this paper to investigate the statistical robustness of the kernel learning estimator (the regularized empirical risk minimizer). We begin by deriving qualitative statistical robustness of the estimator for a broad class of convex loss functions when all of the training data are potentially perturbed under some topological structures, and then move on to consider the quantitative statistical robustness of the estimator for a specific case that the loss function is twice continuously differentiable and convex. In the latter case, we derive the first-order optimality condition of the regularized expected risk minimization problem, which is essentially a stochastic variational inequality problem (SVIP) in RKHS, and then use the SVIP as a platform to investigate local and global Lipschitz continuity of the regularized risk minimizer against perturbation of the probability distribution under the Fortet-Mourier metric. A crucial assumption in the analysis is that the perturbed data are independent and identically distributed. In some practical applications, this assumption may not be fulfilled if a small proportion of perceived data is seriously perturbed/contaminated. In this case, we use the influence function to investigate the impact of single data perturbation on the regularized risk minimizer. Differing from Steinwart and Christmann [70, Chapter 10], we concentrate on constrained expected risk minimization problems. The research is essentially down to the derivation of the implicit function theorem of the SVIP in RKHS. Finally, we illustrate our theoretical analysis with a couple of academic examples.

报告人简介：孙海琳博士是南京师范大学6776永利集团教授。他于2007年在吉林大学获得统计学学士学位，2013年毕业于哈尔滨工业大学，获数学博士学位。在其博士期间，他在英国南安普顿大学和香港理工大学联合培养。2015-2017年在香港理工大学应用数学系做博士后研究。2026年获江苏省青年科技奖，2018年获中国运筹学会青年科技奖和江苏省数学成就奖，主持国家自然科学基金青年科学基金（B类、C类）项目、面上项目以及国家重点研发计划课题。他的研究领域包括随机优化，分布鲁棒优化、随机变分不等式及其在投资组合、风险管理和经济学模型上的应用。他在包括《Mathematical Programming》、《SIAM Journal on Optimization》、《Mathematics of Operations Research》等国际权威期刊发表了二十多篇论文，担任《运筹学学报》、《计算数学》、《Journal of Optimization Theory and Applications》、《Asia-Pacific Journal of Operational Research》、《Numerical Algebra, Control and Optimization》等期刊编委。