Aggregated Hold-Out

TL;DR

Aggregated hold-out (Agghoo) is a new method that combines hold-out and aggregation techniques, with theoretical guarantees and practical improvements over traditional hold-out and cross-validation methods.

Contribution

This paper provides the first theoretical guarantees for Agghoo, demonstrating its safety and effectiveness across various risk minimization problems.

Findings

Agghoo performs at worst like the hold-out in convex risk settings.

Aggregation significantly improves over the hold-out method.

Agghoo is competitive with cross-validation in numerical experiments.

Abstract

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.