@conference {654798,
	title = {Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization},
	booktitle = {Conference on Neural Information Processing Systems (NeurIPS)},
	year = {2020},
	month = {2020},
	abstract = {We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random iid inputs. We study the generalization performances of standard classifiers in the high-dimensional regime where\&nbsp;α=n/d\&nbsp;is kept finite in the limit of a high dimension\&nbsp;d\&nbsp;and number of samples\&nbsp;n. Our contribution is three-fold: First, we prove a formula for the generalization error achieved by\&nbsp;l2\&nbsp;regularized classifiers that minimize a convex loss. This formula was first obtained by the heuristic replica method of statistical physics. Secondly, focussing on commonly used loss functions and optimizing the\&nbsp;l2\&nbsp;regularization strength, we observe that while ridge regression performance is poor, logistic and hinge regression are surprisingly able to approach the Bayes-optimal generalization error extremely closely. As\&nbsp;α{\textrightarrow}$\infty$\&nbsp;they lead to Bayes-optimal rates, a fact that does not follow from predictions of margin-based generalization error bounds. Third, we design an optimal loss and regularizer that provably leads to Bayes-optimal generalization error.},
	url = {https://arxiv.org/abs/2006.06560},
	author = {B. Aubin and Lu, Y.M. and F. Krzakala and L. Zdeborav{\'a}}
}
