报告题目：Mathematical Foundations of Outcome Weighted Learning in Precision Medicine

报告人：向道红 教授 浙江师范大学

邀请人：白艺光

报告时间：2023年4月28日（周五）9:00-10:00

腾讯会议：377-915-430

报告人简介：向道红，浙江师范大学数学科学学院教授，博士生导师，德国洪堡学者，浙江省高校中青年学科带头人，浙江省应用数学研究会副理事长。于2009年2月获香港城市大学博士学位，2009-2010年在香港中文大学作博士后，2010年3月入职浙江师范大学至今。研究领域为统计学习理论、稳健统计等。在《Journal of Machine Learning Research》、《Journal of Approximation Theory》、《Advances in Computational Mathematics》、《Journal of Multivariate Analysis》、《Science China Mathematics》等国内外学术刊物上发表论文多篇。主持完成国家自然科学基金面上项目2项，青年基金1项。

报告摘要： The goal of precision medicine is to determine the optimal individualized treatment rules by considering the heterogeneity of patients, so as to maximize the expected clinical outcome. Outcome weighted learning (OWL) is one of the algorithms to estimate the optimal individualized treatment rules. In this talk we mainly study the convergence theory of OWL associated with varying Gaussians and general convex loss. Fisher consistency of OWL with convex loss is proved by making full use of the convexity of the loss function. Under some noise condition on distributions, quantitative relationship between weighted misclassification error and weighted generalization error is proved. The sample error is estimated by using a projection operator and a tight bound for the covering numbers of reproducing kernel Hilbert spaces generated by Gaussian kernels. Fast learning rates of OWL associated with least square loss, exponential-hinge loss and -norm SVM loss are derived explicitly. We also consider the case of unbounded clinical outcome. Fast learning rates are given by imposing some moment conditions on the clinical outcome.