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Scrambled Objects for Least-Squares Regression

Odalric Maillard 1 Rémi Munos 1
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : We consider least-squares regression using a randomly generated subspace G of finite dimension P, where F is a function space of infinite dimension, e.g.~L₂([0,1]^d). G is defined as the span of P random features that are linear combinations of the basis functions of F weighted by random Gaussian i.i.d.~coefficients. In particular, we consider multi-resolution random combinations at all scales of a given mother function, such as a hat function or a wavelet. In this latter case, the resulting Gaussian objects are called scrambled wavelets and we show that they enable to approximate functions in Sobolev spaces H^s([0,1]^d). An interesting aspect of the resulting bounds is that they do not depend on the distribution from which the data are generated, which is important in a statistical regression setting considered here. Randomization enables to adapt to any possible distribution.
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Submitted on : Friday, February 7, 2014 - 8:23:57 AM
Last modification on : Saturday, December 18, 2021 - 3:03:01 AM


  • HAL Id : hal-00943121, version 1



Odalric Maillard, Rémi Munos. Scrambled Objects for Least-Squares Regression. Advances in Neural Information Processing Systems, 2010, Granada, Spain. ⟨hal-00943121⟩



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