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Grouped Orthogonal Matching Pursuit for Variable Selection and Prediction

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Authors: Grzegorz Swirszcz,Naoki Abe,Aurelie C. Lozano
Where published: NeurIPS 2009 12
Document:  PDF  DOI 
Abstract URL: http://papers.nips.cc/paper/3878-grouped-orthogonal-matching-pursuit-for-variable-selection-and-prediction

We consider the problem of variable group selection for least squares regression, namely, that of selecting groups of variables for best regression performance, leveraging and adhering to a natural grouping structure within the explanatory variables. We show that this problem can be efficiently addressed by using a certain greedy style algorithm. More precisely, we propose the Group Orthogonal Matching Pursuit algorithm (Group-OMP), which extends the standard OMP procedure (also referred to as ``forward greedy feature selection algorithm for least squares regression) to perform stage-wise group variable selection. We prove that under certain conditions Group-OMP can identify the correct (groups of) variables. We also provide an upperbound on the $l_\infty$ norm of the difference between the estimated regression coefficients and the true coefficients. Experimental results on simulated and real world datasets indicate that Group-OMP compares favorably to Group Lasso, OMP and Lasso, both in terms of variable selection and prediction accuracy.

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