%0 Journal Article %1 mignacco2020regularization %A Mignacco, Francesca %A Krzakala, Florent %A Lu, Yue M. %A Zdeborová, Lenka %D 2020 %K noise probability readings regularisation %T The role of regularization in classification of high-dimensional noisy Gaussian mixture %U http://arxiv.org/abs/2002.11544 %X 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.

@article{mignacco2020regularization, 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.}, added-at = {2020-02-28T01:45:54.000+0100}, author = {Mignacco, Francesca and Krzakala, Florent and Lu, Yue M. and Zdeborová, Lenka}, biburl = {https://www.bibsonomy.org/bibtex/2d5fb0d4563b9d6b755482bfc4617a1e1/kirk86}, description = {[2002.11544] The role of regularization in classification of high-dimensional noisy Gaussian mixture}, interhash = {16b45522409c70b29752cb925d35f939}, intrahash = {d5fb0d4563b9d6b755482bfc4617a1e1}, keywords = {noise probability readings regularisation}, note = {cite arxiv:2002.11544Comment: 8 pages + appendix, 6 figures}, timestamp = {2020-02-28T01:45:54.000+0100}, title = {The role of regularization in classification of high-dimensional noisy Gaussian mixture}, url = {http://arxiv.org/abs/2002.11544}, year = 2020 }