Competing against the Best Nearest Neighbor Filter in Regression

Arnak S. Dalalyan 1, 2 Joseph Salmon 3
1 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : Designing statistical procedures that are provably almost as accurate as the best one in a given family is one of central topics in statistics and learning theory. Oracle inequalities offer then a convenient theoretical framework for evaluating different strategies, which can be roughly classified into two classes: selection and aggregation strategies. The ultimate goal is to design strategies satisfying oracle inequalities with leading constant one and rate-optimal residual term. In many recent papers, this problem is addressed in the case where the aim is to beat the best procedure from a given family of linear smoothers. However, the theory developed so far either does not cover the important case of nearest-neighbor smoothers or provides a suboptimal oracle inequality with a leading constant considerably larger than one. In this paper, we prove a new oracle inequality with leading constant one that is valid under a general assumption on linear smoothers allowing, for instance, to compete against the best nearest-neighbor filters.
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https://hal-enpc.archives-ouvertes.fr/hal-00654276
Contributeur : Arnak Dalalyan <>
Soumis le : mercredi 21 décembre 2011 - 14:51:49
Dernière modification le : mercredi 20 février 2019 - 18:14:03

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Arnak S. Dalalyan, Joseph Salmon. Competing against the Best Nearest Neighbor Filter in Regression. ALT 2011 - 22nd International Conference on Algorithmic Learning Theory, Oct 2011, Espoo, Finland. pp.129-143, ⟨10.1007/978-3-642-24412-4_13⟩. ⟨hal-00654276⟩

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