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  k-NN Regression Adapts to Local Intrinsic Dimension

Kpotufe, S. (2012). k-NN Regression Adapts to Local Intrinsic Dimension. In J. Shawe-Taylor, R. Zemel, P. Bartlett, F. Pereira, & K. Weinberger (Eds.), Advances in Neural Information Processing Systems 24 (pp. 729-737). Red Hook, NY, USA: Curran.

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 Creators:
Kpotufe, S1, Author              
Affiliations:
1Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, DE, ou_1497647              

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 Abstract: Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that k-NN regression is also adaptive to intrinsic dimension. In particular our rates are local to a query x and depend only on the way masses of balls centered at x vary with radius. Furthermore, we show a simple way to choose k = k(x) locally at any x so as to nearly achieve the minimax rate at x in terms of the unknown intrinsic dimension in the vicinity of x. We also establish that the minimax rate does not depend on a particular choice of metric space or distribution, but rather that this minimax rate holds for any metric space and doubling measure.

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 Dates: 2012-01
 Publication Status: Published in print
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 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: Kpotufe2012
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Title: Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS 2011)
Place of Event: Granada, Spain
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Title: Advances in Neural Information Processing Systems 24
Source Genre: Proceedings
 Creator(s):
Shawe-Taylor, J, Editor
Zemel, RS, Editor
Bartlett, P, Editor
Pereira, F, Editor
Weinberger, KQ, Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 729 - 737 Identifier: ISBN: 978-1-618-39599-3