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The role of regularization in classification of high-dimensional noisy Gaussian mixture
- Source :
- International Conference on Machine Learning, ICML 2020
- Publication Year :
- 2020
-
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.<br />Comment: 8 pages + appendix, 6 figures
Details
- Database :
- arXiv
- Journal :
- International Conference on Machine Learning, ICML 2020
- Publication Type :
- Report
- Accession number :
- edsarx.2002.11544
- Document Type :
- Working Paper