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Abstract Details

Activity Number: 509
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #306242
Title: Variable Selection via L1 Penalized LAD Method
Author(s): Lie Wang*+
Companies: Massachusetts Institute of Technology
Address: 77 Massachusetts Avenue, Cambridge, MA, 02139, United States
Keywords: variable selection ; L-1 penalized LAD ; stable ; Lasso ; high-dimensional sparse model
Abstract:

We consider the high-dimensional sparse linear regression model, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different from most of other methods, the L1 penalized LAD method does not need any knowledge of standard deviation of the noises or any moment assumptions of the noises. Our analysis shows that the method achieves near oracle performance, i.e. i.e. with large probability, the L2 norm of the estimation error is of order $\sqrt{k \log p/n}$. The result is true for a wide range of noise distributions, even for the Cauchy distribution.


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