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A Data-Dependent Weighted LASSO Under Poisson Noise

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WeightedLassoArxiv(1).pdf (635.1Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
Weighted LASSO; Poisson noise; compressed sensing; genetic motifs; photon-limited imaging
Journal issue
IEEE Transactions on Information Theory
Volume
65
Number
3
Publication date
03-2019
Article pages
1589-1613
Publisher
IEEE - Institute of Electrical and Electronics Engineers
DOI
http://dx.doi.org/10.1109/TIT.2018.2869578
URI
https://basepub.dauphine.fr/handle/123456789/19685
Collections
  • CEREMADE : Publications
Metadata
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Author
Hunt, Xin Jiang
24804 Department of Electrical and Computer Engineering [Durham] [ECE]
Reynaud-Bouret, Patricia
199970 Laboratoire Jean Alexandre Dieudonné [JAD]
Rivoirard, Vincent
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Sansonnet, Laure
135757 Mathématiques et Informatique Appliquées [MIA-Paris]
Willett, Rebecca
24804 Department of Electrical and Computer Engineering [Durham] [ECE]
Type
Article accepté pour publication ou publié
Abstract (EN)
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 1) sidesteps the technical challenges present in previous work, 2) admits estimators that can readily be computed using off-the-shelf LASSO algorithms, and 3) hints at a general framework for broad classes of noise in sparse linear inverse problems. At the heart of this new approach lies a weighted LASSO estimator for which data-dependent weights are based on Poisson 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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