Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

Paper Supplemental

Bibtek download is not available in the pre-proceeding


Authors

Yuan Cao, Quanquan Gu, Mikhail Belkin

Abstract

Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifier for linear classification problems. Specifically, we consider data generated from sub-Gaussian mixtures, and provide a tight risk bound for the maximum margin linear classifier in the over-parameterized setting. Our results precisely characterize the condition under which benign overfitting can occur in linear classification problems, and improve on previous work. They also have direct implications for over-parameterized logistic regression.