Minimum-Norm Interpolation Under Covariate Shift: Theoretical Analysis and Empirical Insights

The core message of this paper is to provide the first non-asymptotic, instance-wise risk bounds for covariate shifts in interpolating linear regression when the source covariance matrix satisfies benign overfitting conditions. The authors use these risk bounds to propose a taxonomy of covariate shifts, showing how the ratio of target eigenvalues to source eigenvalues and the degree of overparameterization affect whether a shift is beneficial or malignant for out-of-distribution generalization.