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Conference Papers Year : 2010

Scrambled Objects for Least-Squares Regression

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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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hal-00943121 , version 1 (07-02-2014)


  • 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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