Sparsity by Worst-Case Penalties
This provides a computationally efficient solution for small to medium-sized sparse modeling problems, improving interpretability through accurate support recovery.
The paper tackles the computational inefficiency of sparse penalty optimization by proposing a new interpretation of elastic-net and group-lasso penalties, resulting in a unified optimization strategy that achieves machine precision accuracy in the time competitors take for rough estimates.
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our experiments demonstrate that this strategy, implemented on the elastic-net, is computationally extremely efficient for small to medium size problems. Our accompanying software solves problems very accurately, at machine precision, in the time required to get a rough estimate with competing state-of-the-art algorithms. We illustrate on real and artificial datasets that this accuracy is required to for the correctness of the support of the solution, which is an important element for the interpretability of sparsity-inducing penalties.