A Pseudo-Boolean Set Covering Machine

The Set Covering Machine (SCM) is a machine learning algorithm that constructs a conjunction of Boolean functions. This algorithm is motivated by the minimization of a theoretical bound. However, finding the optimal conjunction according to this bound is a combinatorial problem. The SCM approximates the solution using a greedy approach. Even though SCM seems very efficient in practice, it is unknown how it compares to the optimal solution. To answer this question, we present a novel pseudo-Boolean optimization model that encodes the minimization problem. It is the first time a Constraint Programming approach addresses the combinatorial problem related to this machine learning algorithm. Using that model and recent pseudo-Boolean solvers, we empirically show that the greedy approach is surprisingly close to the optimal.