Open Access
February 2013 Spatially-adaptive sensing in nonparametric regression
Adam D. Bull
Ann. Statist. 41(1): 41-62 (February 2013). DOI: 10.1214/12-AOS1064


While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise retains the spatial adaptivity properties of a uniform design.


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Adam D. Bull. "Spatially-adaptive sensing in nonparametric regression." Ann. Statist. 41 (1) 41 - 62, February 2013.


Published: February 2013
First available in Project Euclid: 5 March 2013

zbMATH: 1347.62059
MathSciNet: MR3059409
Digital Object Identifier: 10.1214/12-AOS1064

Primary: 62G08
Secondary: 62G20 , 62L05

Keywords: Active learning , adaptive sensing , Nonparametric regression , sequential design , Spatial adaptation , spatially inhomogeneous functions

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • February 2013
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