{"ID":2835226,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00549","arxiv_id":"2512.00549","title":"Convergence Analysis of function-on-function Polynomial regression model","abstract":"In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regularization under a general smoothness condition without imposing any additional conditions on the index function. We also establish lower bounds for any learning algorithm to explain the optimality of our convergence rates.","short_abstract":"In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regulariza...","url_abs":"https://arxiv.org/abs/2512.00549","url_pdf":"https://arxiv.org/pdf/2512.00549v1","authors":"[\"Naveen Gupta\",\"Sivananthan Sampath\"]","published":"2025-11-29T16:42:41Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}