Group-level support recovery guarantees for group lasso estimator

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2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), ISSN: 1520-6149, Page: 4366-4370

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Mojtaba Kadkhodaie Elyaderani, Swayambhoo Jain, Jeffrey Druce, Stefano Gonella, Jarvis Haupt
Institute of Electrical and Electronics Engineers (IEEE)
Computer Science, Engineering
conference paper description
This paper considers the problem of estimating an unknown high dimensional signal from (typically low-dimensional) noisy linear measurements, where the desired unknown signal is assumed to possess a group-sparse structure, i.e. given a (pre-defined) partition of its entries into groups, only a small number of such groups are non-zero. Assuming the unknown group-sparse signal is generated according to a certain statistical model, we provide guarantees under which it can be efficiently estimated via solving the well-known group Lasso problem. In particular, we demonstrate that the set of indices for non-zero groups of the signal (called the group-level support of the signal) can be exactly recovered by solving the proposed group Lasso problem provided that its constituent non-zero groups are small in number and possess enough energy. Our guarantees rely on the well-conditioning of measurement matrix, which is expressed in terms of the block coherence parameter and can be efficiently computed. Our results are non-asymptotic in nature and therefore applicable to practical scenarios.

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