Distributionally robust optimization for credible learning in predictive health applications

Abstract

Data-driven predictive models are increasingly used in clinical settings, but adoption hinges on both interpretability and credibility —i.e., alignment with domain knowledge. For tabular electronic health records data, conventional deep models are hard to interpret, while sparse linear models may sacrifice accuracy or disregard expert guidance. We formulate credible supervised learning as a Distributionally Robust Optimization (DRO) problem with a tailored DRO-expert norm. The norm promotes dense use of an expert-identified group of predictors while encouraging group-wise sparsity elsewhere, recovering a Group LASSO–type penalty. We handle both non-overlapping groups and overlapping groups using latent-variable decompositions. We evaluate on synthetic data by varying predictor correlation and signal-to-noise ratio (SNR), as well as on two real-world healthcare tasks: (i) ICU admission risk for COVID-19 patients and (ii) identification of uncontrolled hypertension from socio-demographic variables. Beyond AUC and F1-score, we report model sparsity and an explicit credibility metric (fraction of expert features retained). Across synthetic studies, the DRO-expert approach yields the most stable and accurate estimation—consistently improving Mean Absolute Error (MAE), Relative Risk, Relative Test Error, and Proportion of Variance Explained (PVE)—especially under high correlation or low SNR; the overlapping variant is strongest overall. On COVID-19 ICU prediction, the overlapping DRO-expert achieves an AUC of 95.85% (+1.86%), an F1-score of 81.28% (+6.90%), and high credibility of 0.86 (+0.10), consistently outperforming the baseline. On uncontrolled hypertension, the overlapping DRO-expert achieves an AUC of 74.90% (+2.44%), an F1 score of 82.35% (+0.31%), and credibility of 0.58 (+0.39), offering the best accuracy–interpretability trade-off among the sparse models while retaining high credibility. The proposed DRO-expert framework integrates expert knowledge into a principled DRO objective, achieving a favorable trade-off among accuracy, interpretability, and credibility. It is robust to correlation, outliers, and distributional mismatch, and is practical for healthcare analytics with grouped and overlapping features.