# Black-Box Model Confidence Sets Using Cross-Validation with High-Dimensional Gaussian Comparison

arXiv: https://arxiv.org/abs/2211.04958 · HTML: https://mlsanity.com/paper/2211.04958/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Is Algorithmic Stability Testable? A Unified Framework under Computational Constraints](https://mlsanity.com/paper/2405.15107/) (2024)
- [Throwing Vines at the Wall: Structure Learning via Random Search](https://mlsanity.com/paper/2510.20035/) (2025)

## Abstract (arXiv)

We derive high-dimensional Gaussian comparison results for the standard V-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with the high-dimensional Gaussian comparison framework for sums of independent random variables. These results give new insights into the joint sampling distribution of cross-validated risks in the context of model comparison and tuning parameter selection, where the number of candidate models and tuning parameters can be larger than the fitting sample size. As a consequence, our results provide theoretical support for a recent methodological development that constructs model confidence sets using cross-validation.