AISTATS 2015poster53 citations
A Bayes consistent 1-NN classifier
Abstract
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1-NN enjoys considerable statistical and algorithmic advantages over the k-NN classifier. These include user-friendly finite-sample error bounds, as well as time- and memory-efficient learning and test-point evaluation algorithms with a principled speed-accuracy tradeoff. Encouraging empirical results are reported.
BibTeX
@InProceedings{pmlr-v38-kontorovich15,
title = {{A Bayes consistent 1-NN classifier}},
author = {Kontorovich, Aryeh and Weiss, Roi},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {480--488},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/kontorovich15.pdf},
url = {https://proceedings.mlr.press/v38/kontorovich15.html},
abstract = {We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1-NN enjoys considerable statistical and algorithmic advantages over the k-NN classifier. These include user-friendly finite-sample error bounds, as well as time- and memory-efficient learning and test-point evaluation algorithms with a principled speed-accuracy tradeoff. Encouraging empirical results are reported.}
}