A1670
Title: Asymptotics of empirical risk minimization in High dimension
Authors: Cosme Jean Leon Louart - Chinese university of Hong Kong Shenzhen (China) [presenting]
Abstract: Recent results on the asymptotic behavior of regularized empirical risk minimization are presented. A complete theoretical characterization of its performance is derived under weak smoothness and convexity assumptions on the loss functions, together with general concentration assumptions on the data. More specifically, a central limit theorem for the minimizer yields an approximation of the test score in a Gaussian-convoluted form involving two deterministic parameters, which are characterized as solutions of a fixed-point equation depending on the population statistics and the loss functions. This approximation makes it possible to fully characterize the breakdown of Gaussian universality for the score, a phenomenon that has attracted significant attention in recent years. The main insights provided by these formulas for several loss functions and models commonly used in practice are discussed.
