Learning Optimized Risk Scores on Large-Scale Datasets

Risk scores are simple classification models that let users quickly assess risk by adding, subtracting and multiplying a few small numbers. These models are used for high-stakes applications in healthcare and criminology, but are difficult to learn from data because they need to be risk-calibrated, use small integer coefficients, and obey operational constraints. In this paper, we present a new approach to learn optimized risk scores from data by solving a discrete optimization problem. We formulate the risk score problem as a mixed integer nonlinear program, and present a new cutting plane algorithm to efficiently recover the optimal solution while avoiding the stalling behavior that occurs when we use existing cutting plane algorithms on non-convex problems. We pair our cutting plane algorithm with specialized procedures to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. The resulting approach can learn optimized risk scores in a way that scales linearly in the number of samples, provides a proof of optimality, and accommodates complex operational constraints. We illustrate the benefits of our approach through extensive numerical experiments.