On the Consistency of Feature Selection using Greedy Least Squares Regression
The Journal of Machine Learning Research
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
New bounds for restricted isometry constants
IEEE Transactions on Information Theory
Asymptotic analysis of robust LASSOs in the presence of noise with large variance
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
IEEE Transactions on Information Theory
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In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L"1 penalized least absolute deviation method. Different from most of the other methods, the L"1 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. with large probability, the L"2 norm of the estimation error is of order O(klogp/n). The result is true for a wide range of noise distributions, even for the Cauchy distribution. Numerical results are also presented.