A data-dependent weighted LASSO under Poisson noise
arXiv:1509.08892
Abstract
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 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 in previous work, (b) admits estimators that can readily be computed using off-the-shelf LASSO algorithms, and (c) 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.
arXiv comment25 pages (48 pages with appendix), 3 figures
References in corpus (11)
- Simultaneous analysis of Lasso and Dantzig selector
- A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers
- Exponential and moment inequalities for U-statistics
- Compressed sensing performance bounds under Poisson noise
- "Pre-conditioning" for feature selection and regression in high-dimensional problems
- Supernova Ejecta in the Youngest Galactic Supernova Remnant G1.9+0.3
- Performance bounds for expander-based compressed sensing in Poisson noise
- Adaptive Lasso and group-Lasso for functional Poisson regression
- Minimax Optimal Sparse Signal Recovery with Poisson Statistics
- Spatio-temporal Compressed Sensing with Coded Apertures and Keyed Exposures
- Minimax optimal convex methods for Poisson inverse problems under -ball sparsity