  In linear regression with fixed design, we propose two procedures that
aggregate a data-driven collection of supports. The collection is a subset of
the $2^p$ possible supports and both its cardinality and its elements can
depend on the data. The procedures satisfy oracle inequalities with no
assumption on the design matrix. Then we use these procedures to aggregate the
supports that appear on the regularization path of the Lasso in order to
construct an estimator that mimics the best Lasso estimator. If the restricted
eigenvalue condition on the design matrix is satisfied, then this estimator
achieves optimal prediction bounds. Finally, we discuss the computational cost
of these procedures.
