Aggregated Hold-Out

Guillaume Maillard (1, 2) , Sylvain Arlot (1, 2) , Matthieu Lerasle (1, 2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CELESTE - Statistique mathématique et apprentissage

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.

Mots clés: regularized kernel regression; bagging; aggregation; hyperparameter selection; cross-validation

Domaines: Statistiques [math.ST]; Machine Learning [stat.ML]; Théorie [stat.TH]; Méthodologie [stat.ME]

Guillaume Maillard, Sylvain Arlot, Matthieu Lerasle. Aggregated Hold-Out. Journal of Machine Learning Research, 2021, 22 (20), pp.1--55. ⟨hal-02273193⟩