Teacher-student models provide a framework in which the typical-case performance of high-
dimensional supervised learning can be described in closed form. The assumptions of …

The class of random features is one of the most popular techniques to speed up kernel
methods in large-scale problems. Related works have been recognized by the NeurIPS Test …

We propose that investment strategies should be evaluated based on their net-oftrading-cost
return for each level of risk, which we term the “implementable efficient frontier.” While …

Predicting groundwater levels is pivotal in curbing overexploitation and ensuring effective
water resource governance. However, groundwater level prediction is intricate, driven by …

In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design.
Exponents for the decay of the excess generalization error of KRR have been reported in …

This paper explores the generalization loss of linear regression in variably parameterized
families of models, both under-parameterized and over-parameterized. We show that the …

We study the spectrum of inner-product kernel matrices, ie, $ n\times n $ matrices with
entries $ h (\langle\textbf {x} _i,\textbf {x} _j\rangle/d) $ where the $(\textbf {x} _i) _ {i\leq n} …

Existing statistical learning guarantees for general kernel regressors often yield loose
bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in a …

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU
activation functions and proves that when the data distribution is well-separated, DNNs can …

In these six lectures, we examine what can be learnt about the behavior of multi-layer neural
networks from the analysis of linear models. We first recall the correspondence between …