  A number of recent work studied the effectiveness of feature selection using
Lasso. It is known that under the restricted isometry properties (RIP), Lasso
does not generally lead to the exact recovery of the set of nonzero
coefficients, due to the looseness of convex relaxation. This paper considers
the feature selection property of nonconvex regularization, where the solution
is given by a multi-stage convex relaxation scheme. Under appropriate
conditions, we show that the local solution obtained by this procedure recovers
the set of nonzero coefficients without suffering from the bias of Lasso
relaxation, which complements parameter estimation results of this procedure.
