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October 2017 “Local” vs. “global” parameters—breaking the Gaussian complexity barrier
Shahar Mendelson
Ann. Statist. 45(5): 1835-1862 (October 2017). DOI: 10.1214/16-AOS1510

Abstract

We show that if $F$ is a convex class of functions that is $L$-sub-Gaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by “local” covering estimates of the class (i.e., the covering number at a specific level), rather than by the Gaussian average, which takes into account the structure of $F$ at an arbitrarily small scale. To that end, we establish new sharp upper and lower estimates on the error rate in such learning problems.

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Shahar Mendelson. "“Local” vs. “global” parameters—breaking the Gaussian complexity barrier." Ann. Statist. 45 (5) 1835 - 1862, October 2017. https://doi.org/10.1214/16-AOS1510

Information

Received: 1 October 2015; Revised: 1 August 2016; Published: October 2017
First available in Project Euclid: 31 October 2017

zbMATH: 06821111
MathSciNet: MR3718154
Digital Object Identifier: 10.1214/16-AOS1510

Subjects:
Primary: 60G15 , 62C20 , 62G08

Keywords: covering numbers , error rates , Gaussian averages

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 5 • October 2017
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