Before revision:  Investigating the synergies between sparse regression solvers and basis adaptivity schemes, we find that virtually all basis-adaptive schemes outperform a static choice of basis. Three sparse solvers, namely Bayesian compressive sensing and two variants of subspace pursuit, perform especially well. Aggregating our results by model dimensionality and experimental design size  , we identify combinations of methods that are most promising for the specific problem class .
After revision:  Investigating the synergies between sparse regression solvers and basis adaptivity schemes, we find that virtually all basis-adaptive scheme is very important, as it can result in more than one order of magnitude difference in performance. No single method significantly outperforms the others, but dividing the analysis into classes (regarding input dimension and experimental design size , we identify combinations of methods that are most promising for the specific problem class .