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

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 go to infinity while their ratio is fixed to α = 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.
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https://hal-cea.archives-ouvertes.fr/cea-02529853
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Submitted on : Thursday, April 2, 2020 - 3:46:20 PM
Last modification on : Wednesday, November 4, 2020 - 3:35:00 AM

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  • HAL Id : cea-02529853, version 1
  • ARXIV : 2002.11544

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Francesca Mignacco, Florent Krzakala, Yue Lu, Lenka Zdeborová. The role of regularization in classification of high-dimensional noisy Gaussian mixture. 2020. ⟨cea-02529853⟩

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