Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression

arXiv:2405.04919v1 Announce Type: cross
Abstract: We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square error for $k$-NN regression is identical to the mean square error of $(k+1)$-NN regression evaluated on the training data, multiplied by the scaling factor $(k+1)^2/k^2$. Therefore, to compute the LOOCV score, one only needs to fit $(k+1)$-NN regression only once, and does not …

abstract arxiv breaking computation cs.ds cs.lg error leave-one-out mean regression show square stat.co stat.me stat.ml type validation