Are Gaussian Data All You Need? The Extents and Limits of Universality in High-Dimensional Generalized Linear Estimation

Luca Pesce, Florent Krzakala, Bruno Loureiro, Ludovic Stephan

Abstract: In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for...