# Weighted Leave-One-Out Cross Validation

arXiv: https://arxiv.org/abs/2505.19737 · HTML: https://mlsanity.com/paper/2505.19737/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 5 of 5)

- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
- [Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions](https://mlsanity.com/paper/2001.10965/) (2020)
- [Fast calculation of Gaussian Process multiple-fold cross-validation residuals and their covariances](https://mlsanity.com/paper/2101.03108/) (2021)
- [Quasi-uniform designs with optimal and near-optimal uniformity constant](https://mlsanity.com/paper/2112.10401/) (2021)

## Abstract (arXiv)

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite collection of sites. The method relies on the construction of the best linear estimator of the squared prediction error at an arbitrary unsampled site based on squared LOO residuals, assuming that the function is a realization of a Gaussian Process (GP). A theoretical analysis of performance of the ISE estimator is presented, and robustness with respect to the choice of the GP kernel is investigated first analytically, then through numerical examples. Overall, the estimation of ISE is significantly more precise than with classical, unweighted, LOO cross validation. Application to model selection is briefly considered through examples.