Statistical Science· 2026Q1
On Neighbourhood Cross Validation
- 1citations
- Q1SCImago
- 2026year
Short summary
A new method efficiently computes and optimizes cross-validation criteria for penalized regression hyperparameters, reducing computational cost to that of a single model fit and enabling leave-out-neighbourhood cross-validation for un-modelled autocorrelation.
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Key points
- Efficient computation and optimization of cross-validation criteria for penalized regression hyperparameters is now possible.
- Computational cost is reduced to be comparable to a single model fit, representing an O(n) saving for n data points.
- Enables leave-out-neighbourhood cross-validation to address un-modelled short-range autocorrelation.
- Accurate uncertainty quantification is achievable even with un-modelled autocorrelation.
AI-generated from the title and abstract; the full text is not read.
Abstract
Many varieties of cross validation would be statistically appealing for the estimation of smoothing and other penalized regression hyperparameters, were it not for the high cost of evaluating such criteria. Here it is shown how to efficiently and accurately compute and optimize a broad variety of cross validation criteria for a wide range of regression models estimated by minimizing a quadratically penalized loss. The leading order computational cost of hyperparameter estimation is made comparable to the cost of a single model fit given hyperparameters. In many cases this represents an O(n) computational saving when modelling n data. The methods make it feasible, for the first time, to use leave-out-neighbourhood cross validation to deal with the widespread problem of un-modelled short range autocorrelation, which otherwise leads to underestimation of smoothing parameters. It is also shown how to accurately quantify uncertainty in this case, despite the un-modelled autocorrelation. Practical examples are provided, including smooth quantile regression, generalized additive models for location scale and shape, and focussing particularly on dealing with un-modelled autocorrelation.
The authors' abstract, as published at the source. Statistical Science, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics