The role of regularization in classification of high-dimensional noisy Gaussian mixture

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

Bibtex »Metadata »Paper »Supplemental »

Bibtek download is not availble in the pre-proceeding


Authors

Francesca Mignacco, Florent Krzakala, Yue Lu, Pierfrancesco Urbani, Lenka Zdeborova

Abstract

We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the generalization error of regularized convex classifiers, including ridge, hinge and logistic regression, in the high-dimensional limit where the number $n$ of samples and their dimension $d$ goes to infinity while their ratio is fixed to $\alpha=n/d$. We discuss surprising effects of the regularization that in some cases allows to reach the Bayes-optimal performances, we illustrate the interpolation peak at low regularization, and analyze the role of the respective sizes of the two clusters.