Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data

תקציר מקורי באנגליתarXiv:2610.07637v1 Announce Type: cross Abstract: Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture this behavior, yet evaluating learning performance under them remains challenging because rare, large feature entries retain non-vanishing effects even in high dimensions. Even in the canonical setting of empirical risk minimization for linear regression with entry-wise i.i.d. symmetric $\alpha$-stable data, a precise asymptotic characterization of prediction has been lacking. In this work, we introduce a functional order parameter that describes the random effective problem associated with each coefficient. Using the replica method, we fully characterize the generalization error in the proportion