ST-BCP: Tightening Coverage Bound for Backward Conformal Prediction via Non-Conformity Score Transformation
This work addresses uncertainty quantification for machine learning practitioners by tightening coverage bounds in a specific incremental improvement to Backward Conformal Prediction.
The paper tackled the problem of a significant gap between estimated and empirical coverage in Backward Conformal Prediction by introducing ST-BCP, a method that uses a data-dependent transformation of nonconformity scores, reducing the average coverage gap from 4.20% to 1.12% on benchmarks.
Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees. While CP yields uncontrolled prediction set sizes, Backward Conformal Prediction (BCP) inverts this paradigm by enforcing a predefined upper bound on set size and estimating the resulting coverage guarantee. However, the looseness induced by Markov's inequality within the BCP framework causes a significant gap between the estimated coverage bound and the empirical coverage. In this work, we introduce ST-BCP, a novel method that introduces a data-dependent transformation of nonconformity scores to narrow the coverage gap. In particular, we develop a computable transformation and prove that it outperforms the baseline identity transformation. Extensive experiments demonstrate the effectiveness of our method, reducing the average coverage gap from 4.20\% to 1.12\% on common benchmarks.