A data-dependent weighted LASSO under Poisson noise
- Others:
- Department of Electrical and Computer Engineering [Durham] (ECE) ; Duke University [Durham]
- Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) ; Université Paris Dauphine-PSL ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)
- Mathématiques et Informatique Appliquées (MIA-Paris) ; Institut National de la Recherche Agronomique (INRA)-AgroParisTech
Description
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.
Additional details
- URL
- https://hal.science/hal-01226837
- URN
- urn:oai:HAL:hal-01226837v1
- Origin repository
- UNICA