Many recent applications in the physical sciences generate large-scale datasets and modern regression techniques are routinely applied to these data for a wide range of purposes. Many of these approaches require a careful choice of a tuning parameter. Often though, simple qualitative and sign-constraints can be imposed on grounds of physical considerations. These constraints simplify the estimation problem as the tuning parameter becomes superfluous. We show the perhaps unexpected effectiveness of this approach for examples in climate science and beyond.
Predictive accuracy is not compromised in general and we examine under which assumptions optimal convergence rates can be achieved.