Competing Against the Best Nearest Neighbor Filter in Regression
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.
Cite
Text
Dalalyan and Salmon. "Competing Against the Best Nearest Neighbor Filter in Regression." International Conference on Algorithmic Learning Theory, 2011. doi:10.1007/978-3-642-24412-4_13Markdown
[Dalalyan and Salmon. "Competing Against the Best Nearest Neighbor Filter in Regression." International Conference on Algorithmic Learning Theory, 2011.](https://mlanthology.org/alt/2011/dalalyan2011alt-competing/) doi:10.1007/978-3-642-24412-4_13BibTeX
@inproceedings{dalalyan2011alt-competing,
title = {{Competing Against the Best Nearest Neighbor Filter in Regression}},
author = {Dalalyan, Arnak S. and Salmon, Joseph},
booktitle = {International Conference on Algorithmic Learning Theory},
year = {2011},
pages = {129-143},
doi = {10.1007/978-3-642-24412-4_13},
url = {https://mlanthology.org/alt/2011/dalalyan2011alt-competing/}
}