Grouplevel support recovery guarantees for group lasso estimator
 Citation data:

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), ISSN: 15206149, Page: 43664370
 Publication Year:
 2017
conference paper description
This paper considers the problem of estimating an unknown high dimensional signal from (typically lowdimensional) noisy linear measurements, where the desired unknown signal is assumed to possess a groupsparse structure, i.e. given a (predefined) partition of its entries into groups, only a small number of such groups are nonzero. Assuming the unknown groupsparse signal is generated according to a certain statistical model, we provide guarantees under which it can be efficiently estimated via solving the wellknown group Lasso problem. In particular, we demonstrate that the set of indices for nonzero groups of the signal (called the grouplevel support of the signal) can be exactly recovered by solving the proposed group Lasso problem provided that its constituent nonzero groups are small in number and possess enough energy. Our guarantees rely on the wellconditioning of measurement matrix, which is expressed in terms of the block coherence parameter and can be efficiently computed. Our results are nonasymptotic in nature and therefore applicable to practical scenarios.