Virtual k-fold cross validation: An effective method for accuracy assessment

LOO and k-fold cross validation are widely used validation methods assessing the accuracy of a model at the expenses of a high computational load (several models need to be trained and performance averaged). To mitigate such phenomenon a virtual LOO method has been suggested in which, by relying on the concept of leverages, provides the LOO estimate of the generalization error in a closed form without the need to re-training different models. In this paper, we extend and generalize such an approach by introducing the virtual k-fold cross validation method which provides a k-fold cross validation estimate without requiring training multiple models. Results, correct for linear models, are approximations for nonlinear ones. Simulation results show the effectiveness of the proposed virtual method which can be suitably extended to cover different figures of merit and performance assessment techniques.