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

Variable Selection with Exponential Weights and $l_0$-Penalization