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  k-NN Regression Adapts to Local Intrinsic Dimension

Kpotufe, S. (2012). k-NN Regression Adapts to Local Intrinsic Dimension. In Advances in Neural Information Processing Systems 24 (pp. 729-737). Red Hook, NY, USA: Curran.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-B87C-1 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-B87D-0
Genre: Conference Paper

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 Creators:
Kpotufe, S1, Author           
Shawe-Taylor, Editor
J., Editor
Zemel, R.S., Editor
Bartlett, P., Editor
Pereira, F., Editor
Weinberger, K.Q., Editor
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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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: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: ISBN: 978-1-618-39599-3
URI: http://nips.cc/Conferences/2011/
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
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Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 729 - 737 Identifier: -