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Conference Papers Year : 2020

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

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Francesca Mignacco
Florent Krzakala
• Function : Author
Yue M. Lu
• Function : Author
• PersonId : 866660
Lenka Zdeborová
• Function : Author

#### 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 $\alpha$ = $n/d$. 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.

#### Domains

Physics [physics]

### Dates and versions

cea-02529853 , version 1 (02-04-2020)

### Identifiers

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

### Cite

Francesca Mignacco, Florent Krzakala, Yue M. Lu, Lenka Zdeborová. The role of regularization in classification of high-dimensional noisy Gaussian mixture. International Conference on Machine Learning, Jun 2020, Virtual event, France. pp.6874-6883. ⟨cea-02529853⟩

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