A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares

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  • Date/Time:
    • Tuesday March 15, 2011
      12:00 pm - 1:00 pm
  • Location: ISyE Executive classroom
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Summary Sentence: A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares

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TITLE:  A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares

SPEAKER: Professor Jinchi Lv

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 $L_0$ 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. This is a joint work with Yingying Fan.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Anita Race
  • Workflow Status: Published
  • Created On: Mar 7, 2011 - 7:37am
  • Last Updated: Oct 7, 2016 - 9:54pm