A Data-Dependent Weighted LASSO

Nov 23

Monday, November 23, 2015

11:00 am - 12:00 pm
Gross Hall 330


Rebecca Willett, UW-Madison

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded or arising from a Gaussian distribution. Poisson observations in particular are a characteristic feature of several real-world applications, including photon-limited imaging systems, network flow tracking, and genetic motif analysis. Previous work on sparse Poisson inverse problems encountered several limiting technical hurdles. I will describe an alternative, streamlined analysis approach for sparse Poisson inverse problems based on a weighted LASSO estimator. This approach (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 broader classes of heteroscedastic 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 admits data-dependent weights, relies on standard conditions on the sensing or design matrix, and allows signal-dependent noise. This is joint work with Xin Jiang, Patricia Reynaud-Bouret, Vincent Rivoirard, and Laure Sansonnet. refreshments served