Mathematics – Statistics Theory
Scientific paper
2009-05-21
Annals of Statistics 2009, Vol. 37, No. 6A, 3498-3528
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS683 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS683
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares estimator enjoys a nonasymptotic property, called the weak oracle property, where the dimensionality can grow exponentially with sample size. For sparse recovery, we present a sufficient condition that ensures the recoverability of the sparsest solution. In particular, we approach both problems by considering a family of penalties that give a smooth homotopy between $L_0$ and $L_1$ penalties. We also propose the sequentially and iteratively reweighted squares (SIRS) algorithm for sparse recovery. Numerical studies support our theoretical results and demonstrate the advantage of our new methods for model selection and sparse recovery.
Fan Yingying
Lv Jinchi
No associations
LandOfFree
A unified approach to model selection and sparse recovery using regularized least squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A unified approach to model selection and sparse recovery using regularized least squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A unified approach to model selection and sparse recovery using regularized least squares will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-324861