Spectral Conformal Risk Control: Distribution-Free Tail Guarantees via Bayesian Quadrature

Modern vision systems are deployed in settings where occasional catastrophic failures matter more than average accuracy—for example in medical imaging, autonomous driving, and safety monitoring. While conformal prediction gives distribution-free uncertainty guarantees, most existing methods only control mean error and are hard to tune toward rare but high-cost mistakes. We propose Bayesian-Quadrature Spectral Risk Control (BQ-SRC), a general framework for controlling tail-focused risks (such as conditional value at risk (CVaR)-style objectives) in a distribution-free way. BQ-SRC views conformal prediction through a Bayesian-quadrature lens and replaces mean-risk control with a flexible family of risk-averse criteria, while keeping the same black-box access to a trained model. A binomial testing scheme reduces the Monte Carlo conservatism of prior approaches, leading to tighter sets without sacrificing guarantees. We evaluate BQ-SRC across diverse vision tasks, including synthetic regression, closed-set and zero-shot image classification, multilabel classification, and semantic segmentation. Across these settings, BQ-SRC consistently maintains finite-sample risk guarantees and often yields smaller or otherwise more informative prediction sets than existing conformal and risk-controlling baselines, sometimes trading a modest amount of efficiency for stronger tail-risk control. We will make our implementation publicly available upon acceptance.