Before revision:  We investigate the synergies between sparse regression solvers and basis adaptivity schemes, and provide recommendations on which of them are most promising for specific classes of problems. Furthermore, we explore the performance of a novel cross-validation-based solver and basis adaptivity selection scheme , which consistently provides close-to-optimal results  .
After revision:  We investigate the synergies between sparse regression solvers and basis adaptivity schemes, and provide recommendations on which of them are most promising for the specific problem class. Additionally, we introduce a novel solver and basis adaptivity selection scheme , which consistently provides close-to-optimal results .