# Cross-Validation for Correlated Data

arXiv: https://arxiv.org/abs/1904.02438 · HTML: https://mlsanity.com/paper/1904.02438/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Latent Gaussian Model Boosting](https://mlsanity.com/paper/2105.08966/) (2021)
- [Risk and cross validation in ridge regression with correlated samples](https://mlsanity.com/paper/2408.04607/) (2024)
- [Fast calculation of Gaussian Process multiple-fold cross-validation residuals and their covariances](https://mlsanity.com/paper/2101.03108/) (2021)
- [High-dimensional analysis of ridge regression for non-identically distributed data with a variance profile](https://mlsanity.com/paper/2403.20200/) (2024)
- [Trees-Based Models for Correlated Data](https://mlsanity.com/paper/2102.08114/) (2021)
- [Latent mixed-effect models for high-dimensional longitudinal data](https://mlsanity.com/paper/2409.11008/) (2024)
- [Fast Gaussian Process Approximations for Autocorrelated Data](https://mlsanity.com/paper/2512.02925/) (2025)
- [Fast leave-one-cluster-out cross-validation using clustered Network Information Criterion (NICc)](https://mlsanity.com/paper/2405.20400/) (2024)
- [Improving Group Lasso for high-dimensional categorical data](https://mlsanity.com/paper/2210.14021/) (2022)
- [S-SIRUS: an explainability algorithm for spatial regression Random Forest](https://mlsanity.com/paper/2408.05537/) (2024)

## Abstract (arXiv)

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-i.i.d. data. This paper analyzes CV for correlated data. We present a criterion for suitability of standard CV in presence of correlations. When this criterion does not hold, we introduce a bias corrected cross-validation estimator which we term CVc, that yields an unbiased estimate of prediction error in many settings where standard CV is invalid. We also demonstrate our results numerically, and find that introducing our correction substantially improves both, model evaluation and model selection in simulations and real data studies.