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- W3100817920 abstract "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 L0 and L1 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." @default.
- W3100817920 created "2020-11-23" @default.
- W3100817920 creator A5034015361 @default.
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- W3100817920 date "2009-12-01" @default.
- W3100817920 modified "2023-10-18" @default.
- W3100817920 title "A unified approach to model selection and sparse recovery using regularized least squares" @default.
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- W3100817920 doi "https://doi.org/10.1214/09-aos683" @default.
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