# Aggregated Hold-Out

arXiv: https://arxiv.org/abs/1909.04890 · HTML: https://mlsanity.com/paper/1909.04890/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

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

- [Targeted Cross-Validation](https://mlsanity.com/paper/2109.06949/) (2021)
- [Medium-Term Multi-Resolution Electric Load Forecasting using Economic Data and Foundation Model](https://mlsanity.com/paper/2609.31806/) (2026)

## Abstract (arXiv)

Aggregated hold-out (Agghoo) is a method which averages learning rules selected by hold-out (that is, cross-validation with a single split). We provide the first theoretical guarantees on Agghoo, ensuring that it can be used safely: Agghoo performs at worst like the hold-out when the risk is convex. The same holds true in classification with the 0-1 risk, with an additional constant factor. For the hold-out, oracle inequalities are known for bounded losses, as in binary classification. We show that similar results can be proved, under appropriate assumptions, for other risk-minimization problems. In particular, we obtain an oracle inequality for regularized kernel regression with a Lip-schitz loss, without requiring that the Y variable or the regressors be bounded. Numerical experiments show that aggregation brings a significant improvement over the hold-out and that Agghoo is competitive with cross-validation.