{"ID":2880734,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13895","arxiv_id":"2508.13895","title":"Generalisation and benign over-fitting for linear regression onto random functional covariates","abstract":"We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the $n$ covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, $4$-th order moment, and other regularity conditions, we obtain probabilistic bounds on a notion of predictive excess risk adapted to our random functional covariate setting, making use of recent results of Barzilai and Shamir. We derive convergence rates in regimes where $p$ grows suitably fast relative to $n$, illustrating interplay between ingredients of the model in determining convergence behaviour and the role of additive covariate noise in benign-overfitting.","short_abstract":"We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assum...","url_abs":"https://arxiv.org/abs/2508.13895","url_pdf":"https://arxiv.org/pdf/2508.13895v1","authors":"[\"Andrew Jones\",\"Nick Whiteley\"]","published":"2025-08-19T15:01:20Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}