Screening for learning classification rules via Boolean compressed sensing

Convex relaxations for sparse representation problems, which aim to find sparse solutions to systems of equations, have enabled a variety of exciting applications in high-dimensional settings. Yet, with dimensions large enough, even these convex formulations become prohibitively expensive. Screening methods attempt to use duality theory to dramatically reduce the size of the optimization problem through easily computable certificates that many of the variables must be zero in the optimal solution. In this paper we consider learning sparse classification rules via Boolean compressed sensing and develop screening procedures that can significantly reduce the size of the resulting linear program. Boolean compressed sensing deals with systems of Boolean equations (instead of linear equations in traditional compressed sensing); we develop screening methods specifically for this setting. We demonstrate the effectiveness of our screening rules on several real-world classification data sets.