Minimax optimality of classical scaling under general noise conditions
Siddharth Vishwanath, Ery Arias-Castro · Information and Inference A Journal of the IMA · 2026
Abstract We establish the consistency of classical scaling under a broad class of noise models, encompassing many commonly studied cases in the literature. Our approach requires finite moments up to order $q> 4$ for the noise, significantly weakening standard assumptions. We derive convergence rates for classical scaling and establish matching minimax lower bounds, demonstrating that classical scaling achieves minimax optimality in recovering the true configuration even when the input dissimilarities are corrupted by noise.