Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm

The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\ell_2$-data error objective and the $\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection process with sparsity models has been precisely the center of attention over the last decade in order to improve learning performance. To this end, we alter the selection process of LASSO to explicitly leverage combinatorial sparsity models (CSMs) via the combinatorial selection and least absolute shrinkage CLASH operator. We provide concrete guidelines how to leverage combinatorial constraints within CLASH, and characterize CLASH's guarantees as a function of the set restricted isometry constants of the sensing matrix. Finally, our experimental results show that CLASH can outperform both LASSO and model-based compressive sensing in sparse estimation.


Published in:
Proceedings of the 2012 IEEE International Symposium on Information Theory (ISIT), 2216 - 2220
Presented at:
2012 IEEE International Symposium on Information Theory Proceedings (ISIT), Cambridge, Massachusetts, USA, July 1-6, 2012
Year:
2012
Publisher:
New York, IEEE
ISBN:
978-1-4673-2579-0
Laboratories:




 Record created 2013-01-14, last modified 2018-03-17

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