PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Sparse recovery with brownian sensing
Alexandra Carpentier, Odalric Maillard and Rémi Munos
NIPS 2011 2011.

Abstract

We consider the problem of recovering the parameter α of a sparse function f (i.e. the number of non-zero entries of α is small compared to the number K of features) given noisy evaluations of f at a set of well-chosen sampling points. We introduce an additional randomization process, called Brownian sensing, based on the computation of stochastic integrals, which produces a Gaussian sensing matrix, for which good recovery properties are proven, independently on the number of sampling points N, even when the features are arbitrarily non-orthogonal. Under the assumption that f is Hölder continuous with exponent at least 1/2 we provide an estimate of the parameter with quadratic error O(||η|| / N ), where η is the observation noise. The method uses a set of sampling points uniformly distributed along a one-dimensional curve selected according to the features. We report numerical experiments illustrating our method.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:COMPLACS
ID Code:8983
Deposited By:Rémi Munos
Deposited On:21 February 2012