Reviews: Boolean Decision Rules via Column Generation

The authors propose a mathematical programming approach to build interpretable machine learning models. In this case, the interpretable model is a system of Boolean rules in disjunctive (or conjunctive) normal form which is constructed using column generation for the linear relaxation of a mixed integer program (MIP) designed to minimize the number of positive samples classified incorrectly and the complexity of the learned system subject to complexity constraints. To remedy the fact that there are exponentially many potential clauses to optimize over, the authors propose a standard column generation approach that prices potential columns to add and solves a secondary integer program to find such potential columns. The authors also note that the column generation can also be done via heuristics or a greedy algorithm. Once the linear programming program is solved or reaches its time limit, the approach then solves the global mixed integer formulation to get a final set of rules.