Fragility-aware Classification for Risk Characterization and Robust Learning

Classification models play a central role in data-driven decision-making applications such as medical diagnosis, recommendation systems, and risk assessment. Traditional performance metrics, such as accuracy and AUC, quantify classification errors and pairwise ranking performance but do not account for the magnitude of errors, i.e., the risk of confident misjudgments. This limitation is particularly consequential in safety-critical and cost-sensitive settings, where overconfident errors can lead to severe outcomes. To address this issue, we propose the Fragility Index (FI), a novel performance metric that evaluates classifiers from a risk-averse perspective by capturing the tail risk of confident misjudgments. We formulate FI within a robust satisficing (RS) framework to quantify classifier sensitivity under distributional uncertainty. Building on this, we develop a tractable surrogate-based training framework and establish provable bounds connecting training fragility to ranking-error FI. We further derive tractable reformulations for a broad class of loss functions, including cross-entropy, hinge-type, and Lipschitz losses, and identify specific conditions under which these reformulations are exact. We also introduce an FI-induced regularizer for deep neural networks. Empirical results on real-world medical diagnosis tasks demonstrate that FI complements existing metrics by revealing error tail risk not reflected in accuracy or AUC. FI-based models achieve competitive predictive performance while generally attaining lower FI. In the simulated human--AI diagnostic workflow, they also achieve lower average operational costs than empirical risk minimization.