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Pré-Publication, Document De Travail Année : 2015

A data-dependent weighted LASSO under Poisson noise

Résumé

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a characteristic feature of several real-world applications. Previous work on sparse Poisson inverse problems encountered several limiting technical hurdles. This paper describes a novel alternative analysis approach for sparse Poisson inverse problems that (a) sidesteps the technical challenges present in previous work, (b) admits estimators that can readily be computed using off-the-shelf LASSO algorithms, and (c) hints at a general weighted LASSO framework for broad classes of problems. At the heart of this new approach lies a weighted LASSO estimator for which data-dependent weights are based on Pois-son concentration inequalities. Unlike previous analyses of the weighted LASSO, the proposed analysis depends on conditions which can be checked or shown to hold in general settings with high probability.
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Dates et versions

hal-01226837 , version 1 (10-11-2015)

Identifiants

  • HAL Id : hal-01226837 , version 1

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Xin Jiang, Patricia Reynaud-Bouret, Vincent Rivoirard, Laure Sansonnet, Rebecca Willett. A data-dependent weighted LASSO under Poisson noise. 2015. ⟨hal-01226837⟩
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