  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.
