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Aggregated Hold-Out

Guillaume Maillard, Sylvain Arlot, Matthieu Lerasle; 22(20):1−55, 2021.

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 Lipschitz 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.

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