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, closedset 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 riskcontrolling baselines, sometimes trading a modest amount of efficiency for stronger tail-risk control. The code will be publicly available at https://github.com/ MohammadMahdiKazemi/BQ_SRC.