The LASSO for generic design matrices as a function of the relaxation parameter

Details The LASSO for generic design matrices as a function of the relaxation parameter The LASSO for generic design matrices as a function of the relaxation parameter

2011-05-07

arxiv.org/abs/1105.1430v1

Mathematics

Statistics Theory

Scientific paper

The LASSO is a variable subset selection procedure in statistical linear regression based on $\ell_1$ penalization of the least-squares operator. Its behavior crucially depends, both in practice and in theory, on the ratio between the fidelity term and the penalty term. We provide a detailed analysis of the fidelity vs. penalty ratio as a function of the relaxation parameter. Our study is based on a general position condition on the design matrix which holds with probability one for most experimental models. Along the way, the proofs of some well known basic properties of the LASSO are provided from this new generic point of view.

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