Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression
<|reference_start|>Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression: 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 need to repeat training-validation of $k$-NN regression for the number of training data. Numerical experiments confirm the validity of the fast computation method.<|reference_end|>
@article{kanagawa2024fast,
    title={Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression},
    author={Motonobu Kanagawa},
    journal={arXiv preprint arXiv:2405.04919},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04919},
    primaryClass={stat.ML cs.DS cs.LG stat.CO stat.ME}
}