Concentration inequalities for cross-validation in scattered data approximation

Choosing models from a hypothesis space is frequent task in approximation theory and inverse problems. Cross-validation classical tool the learner's repertoire to compare goodness of fit for different reconstruction models. Much work has been dedicated computing this quantity fast manner but tackling its theoretical properties occurs be difficult. So far, most optimality results are stated an asymptotic fashion. In paper we propose concentration inequality on difference cross-validation score risk functional with respect squared error. This gives pre-asymptotic bound which holds high probability. For assumptions rely bounds uniform error model allow broadly applicable framework. We support our claims by applying machinery Shepard's model, where able determine precise constants inequality. Numerical experiments combination algorithms indicate applicability results.