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The Role of Regularization in Classification of High-dimensional Noisy Gaussian Mixture
Francesca Mignacco · Florent Krzakala · Yue Lu · Pierfrancesco Urbani · Lenka Zdeborova

Tue Jul 14 01:00 PM -- 01:45 PM & Wed Jul 15 02:00 AM -- 02:45 AM (PDT) @
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 $d$ go 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 also illustrate the interpolation peak at low regularization, and analyze the role of the respective sizes of the two clusters.

Author Information

Francesca Mignacco (IPhT, CEA Saclay)
Florent Krzakala (ENS)
Yue Lu (Harvard University, USA)
Pierfrancesco Urbani (Institut de Physique Théorique)
Lenka Zdeborova (CNRS)

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