We consider a problem of multiclass classification, where the training sample $$ is generated from the model ℙ(Y = m|X = x) = η$$(x), 1 ≤ m ≤ M, and η1(x), …, η$$(x) are unknown α-Holder continuous functions. Given a test point X, our goal is to predict its label. A widely used k-nearest-neighbors classifier constructs estimates of η1(X), …, η$$(X) and uses a plug-in rule for the prediction. However, it requires a proper choice of the smoothing parameter k, which may become tricky in some situations. We fix several integers n1, …, n$$, compute corresponding n$$-nearest-neighbor estimates for each m and each n$$ and apply an aggregation procedure. We study an algorithm, which constructs a convex combination of these estimates such that the aggregated estimate behaves approximately as well as an oracle choice. We also provide a non-asymptotic analysis of the procedure, prove its adaptation to the unknown smoothness parameter α and to the margin and establish rates of convergence under mild assumptions.
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DOI : 10.1051/ps/2019021
Mots-clés : Multiclass classification, k nearest neighbors, adaptive procedures
@article{PS_2020__24_1_69_0,
author = {Puchkin, Nikita and Spokoiny, Vladimir},
title = {An adaptive multiclass nearest neighbor classifier},
journal = {ESAIM: Probability and Statistics},
pages = {69--99},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2019021},
mrnumber = {4069295},
zbl = {1440.62250},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2019021/}
}
TY - JOUR AU - Puchkin, Nikita AU - Spokoiny, Vladimir TI - An adaptive multiclass nearest neighbor classifier JO - ESAIM: Probability and Statistics PY - 2020 SP - 69 EP - 99 VL - 24 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2019021/ DO - 10.1051/ps/2019021 LA - en ID - PS_2020__24_1_69_0 ER -
Puchkin, Nikita; Spokoiny, Vladimir. An adaptive multiclass nearest neighbor classifier. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 69-99. doi : 10.1051/ps/2019021. http://www.numdam.org/articles/10.1051/ps/2019021/
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Cité par Sources :
Financial support by the Russian Academic Excellence Project 5-100 and by the German Research Foundation (DFG) through the Collaborative Research Center 1294 is gratefully acknowledged.
