In this talk, I will establish high‑probability non‑asymptotic upper bounds for the population excess risk of minimum ℓ_q‑norm interpolating estimators in linear regression for all q ≥ 1, and minimum ℓ_2‑norm interpolating classifiers in linear classification under weak moment assumptions. As a result, we obtain sufficient conditions for their benign overfitting behavior. Building upon non‑exact oracle inequalities, we further introduce a new notion, which we refer to as non‑exact benign overfitting, and establish sufficient conditions under which it arises.


Our results rely on a Features Space Decomposition (FSD) method, where the self‑regularization properties of the minimum norm interpolant estimator are highlighted. Technically, we circumvent the convex Gaussian min‑max theorem, instead employing the Dvoretzky–Milman theorem from Geometric Aspects of Functional Analysis (GAFA).


We particularly emphasize that the FSD method may potentially refine the uniform convergence approach, suggesting its promise as a new fundamental methodology in mathematical statistics. The isomorphic Dvoretzky–Milman theorem established in this work under weak moment assumptions for the ℓ_q norm may be of independent interest in GAFA.


This talk is based on a joint work in preparation with Radosław Adamczak, Guillaume Lecué, and Marta Strzelecka.