Speaker: 姚方教授，北京大学

Inviter: 中国科学院数学院学术报告会组委

Title: Semiparametric M-estimation with Overparameterized Neural Networks

Language: Chinese

Time & Venue: 2025.02.21 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: 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, and 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.