A Tale of Two Uncertainties: Global–Local Attribution for Conformal Prediction

Conformal prediction (CP) enables statistically valid uncertainty quantification with finite-sample, distribution-free coverage guarantees. However, due to the conformalization step in CP, the predictive set is shaped not only by the test point but also by the calibration set, leading to the mixing of dataset-level and instance-level effects that complicates instance-level explanations. We address this challenge by introducing a global–local decomposition of conformal interval width, together with a Shapley-based attribution framework that quantifies how each feature, via its realized value, contributes to narrowing or widening the interval, while preserving exact additivity and conservation of total uncertainty. Global attributions capture calibration-driven baseline uncertainty, while local attributions explain instance-specific deviations relative to this baseline. Experiments on synthetic and semi-synthetic datasets show that the explicit decomposition resolves ambiguity in the source of uncertainty and that it can make a substantial impact on decision making.