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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.06927 |
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Table of Contents:
- We revisit the problem of ensuring strong test set performance via cross-validation, and propose a nested k-fold cross-validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an empirical model-stability measure. The weight on the stability term is itself chosen via a nested cross-validation procedure. This reduces the risk of strong validation set performance and poor test set performance due to instability. We benchmark our procedure on a suite of $13$ real-world datasets, and find that, compared to $k$-fold cross-validation over the same hyperparameters, it improves the out-of-sample MSE for sparse ridge regression and CART by $4\%$ and $2\%$ respectively on average, but has no impact on XGBoost. It also reduces the user's out-of-sample disappointment, sometimes significantly. For instance, for sparse ridge regression, the nested k-fold cross-validation error is on average $0.9\%$ lower than the test set error, while the $k$-fold cross-validation error is $21.8\%$ lower than the test error. Thus, for unstable models such as sparse regression and CART, our approach improves test set performance and reduces out-of-sample disappointment.