The extension of Rippa’s algorithm beyond LOOCV

Rippa's algorithm is a well-known Leave-One-Out Cross Validation (LOOCV) scheme that is adopted in Radial Basis Function (RBF) interpolation for the tuning of the shape parameter. Indeed, it provides remarkable advantages concerning the computational cost with respect to a standard implementation. In this paper, we extend such algorithm to work in a more general k-fold CV setting. After providing a theoretical formulation and proving that the proposed scheme computes an exact k-fold CV, we compare it to a standard k-fold CV implementation. Especially when k gets large, the saving in computational cost is evident.