Conformal Non-Coverage Risk Control (CNCRC): Risk-Centric Guarantees for Predictive Safety in High-Stakes Settings

Standard Conformal Prediction (CP) guarantees that prediction sets contain the true label with high probability, but it is cost-blind, treating all errors as equally important---a critical limitation in high-stakes domains. We introduce Conformal Non-Coverage Risk Control (CNCRC), a framework that replaces coverage frequency with direct risk control. CNCRC guarantees an upper bound on catastrophic non-coverage risk while actively reducing ambiguity risk, providing prediction sets that are both safe and usable. This is achieved through a principled decomposition of decision risk and the design of risk-weighted nonconformity scores that balance robustness with efficiency. Experiments show that CNCRC reliably satisfies strict risk constraints in adversarial settings and outperforms all baselines on a large-scale clinical benchmark. By offering practitioners a choice between maximum robustness and maximum efficiency, CNCRC provides a practical and theoretically grounded toolkit for deploying genuinely risk-aware machine learning systems in safety-critical applications. The implementation is uploaded as supplementary material.