Regularized regression and classification methods fit a linear model to data, based on some loss criterion, subject to a constraint on the coefficient values. As special cases, ridge-regression, the lasso, and subset selection all use squared-error loss with different particular constraint choices. For large problems the general choice of loss/constraint combinations is usually limited by the computation required to obtain the corresponding solution estimates, especially when non convex constraints are used to induce very sparse solutions. A fast algorithm is presented that produces solutions that closely approximate those for any convex loss and a wide variety of convex and non convex constraints, permitting application to very large problems. The benefits of this generality are illustrated by examples.

Reception to follow the talk. Location to be announced.