  The popular Lasso approach for sparse estimation can be derived via
marginalization of a joint density associated with a particular stochastic
model. A different marginalization of the same probabilistic model leads to a
different non-convex estimator where hyperparameters are optimized. Extending
these arguments to problems where groups of variables have to be estimated, we
study a computational scheme for sparse estimation that differs from the Group
Lasso. Although the underlying optimization problem defining this estimator is
non-convex, an initialization strategy based on a univariate Bayesian forward
selection scheme is presented. This also allows us to define an effective
non-convex estimator where only one scalar variable is involved in the
optimization process. Theoretical arguments, independent of the correctness of
the priors entering the sparse model, are included to clarify the advantages of
this non-convex technique in comparison with other convex estimators. Numerical
experiments are also used to compare the performance of these approaches.
