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Activity Number:
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51
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Type:
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Invited
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Date/Time:
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Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
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Sponsor:
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ENAR
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| Abstract - #302757 |
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Title:
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A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares
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Author(s):
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Jinchi Lv*+ and Yingying Fan
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Companies:
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University of Southern California and University of Southern California
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Address:
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IOM Department, HOH 504, Los Angeles, CA, 90089,
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Keywords:
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Model selection ; Sparse recovery ; High dimensionality ; Concave penalty ; Regularized least squares ; Weak oracle property
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Abstract:
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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 (RLS) with concave penalties. For model selection, we establish conditions under which a RLS estimator enjoys the nonasymptotic 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 L0 and L1 penalties. We also propose 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.
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