Certifying Query-Local Calibration Contamination for Safe-Pair Prediction under Interventions

This paper aims to construct reliable prediction intervals for intervention–outcome pairs asserted to be causally unaffected. Although working graphs identify candidate negative controls, graph errors can contaminate query-local calibration pools, making global error corrections insufficient. To address this problem, we propose Certified Graph-Local Conformal Prediction (CGLCP), which couples limited random verification with query-specific conformal calibration. For each fixed safe query, we invert the exact hypergeometric law to upper-bound the selected pool's unsafe count and translate this certificate into a conformal rank. Under safe-score exchangeability and exact independent verification, the procedure guarantees finite-sample marginal coverage and uses the smallest certificate-valid rank against arbitrary contaminating scores. We further quantify the efficiency loss relative to an oracle that knows the local contamination count. Simulations and a K562 Perturb-seq study illustrate the resulting trade-offs among coverage, interval width, finite-output availability, and verification cost, supporting the use of calibrated intervals as negative-control diagnostics under interventions.