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Variable Selection with Exponential Weights and l0l_0l0​-Penalization

13 August 2012
E. Arias-Castro
Karim Lounici
ArXiv (abs)PDFHTML
Abstract

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation under the necessary identifiability condition on the design matrix, instead of much stronger assumptions required by other methods such as the Lasso or the Dantzig Selector. The same analysis yields consistency results for Bayesian methods and BIC-type variable selection under similar conditions.

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