Optimal Risk Scores for Continuous Predictors

TL;DR

This paper introduces a new optimization method for creating risk scores that directly handle continuous predictors by selecting optimal thresholds, improving upon previous discretization-based approaches.

Contribution

It presents a novel mixed-integer nonlinear optimization framework that allows continuous predictors to determine their own thresholds, unlike prior methods that rely on arbitrary discretization.

Findings

Effective in synthetic datasets

Outperforms discretization-based methods

Enables direct threshold selection for continuous variables

Abstract

In this paper, we propose a novel Mixed-Integer Non-Linear Optimization formulation to construct a risk score, where we optimize the logistic loss with sparsity constraints. Previous approaches are typically designed to handle binary datasets, where continuous predictor variables are discretized in a preprocessing step by using arbitrary thresholds, such as quantiles. In contrast, we allow the model to decide for each continuous predictor variable the particular threshold that is critical for prediction. The usefulness of the resulting optimization problem is tested in synthetic datasets.