SURPRISES IN HIGH-DIMENSIONAL RIDGELESS LEAST SQUARES INTERPOLATION.

ABSTRACT: Interpolators-estimators that achieve zero training error-have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum ℓ ₂ norm ("ridgeless") interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature distribution: a linear model, where the feature vectors x i ∈ ℝ p are obtained by applying a linear transform to a vector of i.i.d. entries, x _i = Σ^1/2 z _i (with z i ∈ ℝ p ); and a nonlinear model, where the feature vectors are ob

SUBMITTER: Hastie T 

PROVIDER: S-EPMC9481183 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature