Concentration Inequalities for Cross-validation in Scattered Data Approximation
From MaRDI portal
Publication:6368800
DOI10.1016/J.JAT.2022.105715arXiv2105.13790MaRDI QIDQ6368800
Publication date: 28 May 2021
Abstract: Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models. Much work has been dedicated to computing this quantity in a fast manner but tackling its theoretical properties occurs to be difficult. So far, most optimality results are stated in an asymptotic fashion. In this paper we propose a concentration inequality on the difference of cross-validation score and the risk functional with respect to the squared error. This gives a pre-asymptotic bound which holds with high probability. For the assumptions we rely on bounds on the uniform error of the model which allow for a broadly applicable framework. We support our claims by applying this machinery to Shepard's model, where we are able to determine precise constants of the concentration inequality. Numerical experiments in combination with fast algorithms indicate the applicability of our results.
Nonparametric regression and quantile regression (62G08) Nonparametric estimation (62G05) Hypothesis testing in multivariate analysis (62H15) Multidimensional problems (41A63) Spline approximation (41A15)
This page was built for publication: Concentration Inequalities for Cross-validation in Scattered Data Approximation
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6368800)
