CMStatistics 2022: Start Registration
View Submission - CMStatistics
Title: Sup-norm convergence of deep network estimator for nonparametric regression with corrected adversarial training Authors:  Masaaki Imaizumi - The University of Tokyo (Japan) [presenting]
Abstract: The purpose is to study the stability of an estimator for the nonparametric regression problem by deep neural networks and adversarial training. Several studies show that deep neural networks give estimators for the nonparametric problem which theoretically outperform conventional estimators in a specific setting. A limitation of the estimator by deep networks is stability: its convergence is measured by a restricted class of norms. We consider adversarial training for deep networks and develop an estimator for the nonparametric regression problem. We investigate its efficiency by the minimax optimization scheme and derive several convergence rates with different norms. We also discuss an application based on the result.