Abstract
We describe a procedure enhancing L1 -penalized regression by adding dynamically generated rules describing multidimensional “box” sets. Our rule-adding procedure is based on the classical column generation method for highdimensional linear programming. The pricing problem for our column generation procedure reduces to the N P-hard rectangular maximum agreement (RMA) problem of finding a box that best discriminates between two weighted datasets. We solve this problem exactly using a parallel branch-and-bound procedure. The resulting rule-enhanced regression method is computation-intensive, but has promising prediction performance.