讲座题目: Semiparametric M-estimation using Overparameterized Neural Networks

主讲人：姚方 教授（北京大学）

讲座时间：2024年12月8日上午9:50-10:40

讲座地点：深圳大学粤海校区校友广场303会议室

报告内容：Recent advances in deep learning have brought significant success in various domains, but interpretability remains challenges. Semiparametric modeling offers a valid approach to exploit the remarkable learning capabilities of deep neural networks (DNNs) while enabling inference on parameters of interest. However, for semiparametric M-estimation, ensuring that the parametric component exhibits semiparametric efficiency is challenging, mainly due to the nonconvexity and nonlinearity inherent in training DNNs. In this work, we introduce a novel theoretical framework for semiparametric M-estimation using overparameterized neural networks. We analyze the optimization convergence under general loss functions. Regarding the statistical properties of the algorithmic estimators, we derive nonparametric optimal convergence and parametric asymptotic normality for a broad class of loss functions. These results hold without assuming the boundedness of the candidate set and even when the true function does not lie within the specified function class. To illustrate the applicability of the framework, we provide examples from classification and regression, and the numerical experiments empirically support the theoretical findings.

报告人简历：北京大学讲席教授、入选国家高层次人才计划，北大统计科学中心主任、概率统计系主任。国际数理统计学会（IMS）Fellow与理事会理事，美国统计学会（ASA）Fellow，获2024年第六届科学探索奖（数学物理学领域）。2000年本科毕业于中国科技大学统计专业，2003获得加利福尼亚大学戴维斯分校统计学博士学位，曾任职于多伦多大学统计科学系长聘正教授。至今担任9个国际统计学核心期刊的主编或编委，包括《加拿大统计学期刊》主编，顶级期刊《Journal of the American Statistical Association》和《Annals of Statistics》编委等。

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邀请人：数学科学学院（周彦）

                                       数学科学学院

                                2024年12月6日