🤖 AI Summary
This study addresses the critical issue that existing selective prediction methods in signal domains—such as anomalous sound detection and AI-generated image forensics—often yield a false sense of security due to the use of uncalibrated thresholds, resulting in actual error rates that substantially exceed users’ prescribed risk budgets. The work presents the first systematic audit of four distribution-free calibration rules (NAIVE, Hoeffding, Clopper–Pearson, and Betting) regarding their risk control performance on both real and synthetic data. Findings reveal that NAIVE exceeds the risk budget in 49–73% of experiments; Clopper–Pearson and Betting achieve zero violations under exchangeability but suffer 9–30% violation rates when deployed in grouped settings where exchangeability fails. Group-wise thresholding restores valid risk control at the cost of reduced coverage. The study underscores the pivotal role of tight confidence bounds for effective coverage and identifies uncalibrated thresholds as the root cause of risk miscontrol.
📝 Abstract
Selective prediction with distribution-free risk control promises that, with confidence 1-delta over the calibration draw, the error rate of accepted inputs stays below a user budget alpha. We audit this promise on signal-domain detectors -- machine anomalous-sound detection (ASD) and AI-generated-image forensics -- for four calibration rules: uncertified empirical thresholding (NAIVE) and certified Hoeffding, Clopper-Pearson (CP), and betting (WSR) upper confidence bounds. We report three findings. (i) NAIVE thresholding, common in practice, exceeds its declared budget in 49-73% of synthetic trials (n=200 calibration points) and in up to 68% of real-data splits: a false sense of safety rather than a broken theorem, since the rule never had a certificate. (ii) Tightness matters: CP and WSR certify substantial coverage where Hoeffding certifies none, with zero observed budget overruns under exchangeable splits. (iii) Under grouped deployment (unseen machine types or generators), certified rules overrun in 9-30% of trials -- far above delta -- showing the failure lies in the broken exchangeability premise, not in the bounds; a conservative per-group threshold restores validity at a severe coverage cost.