Minxuan Huang

Rui Xu, Xingyuan Chen, Wenxing Huang et al.

Conformal prediction (CP) constructs prediction sets with marginal coverage guarantees under the assumption that the calibration and test distributions are identical. However, under distribution shift, existing approaches primarily align marginal conformal score distributions, which is sufficient to preserve marginal coverage but does not control the conditional coverage error at individual test inputs. As a consequence, CP can remain unreliable in regions where the conditional score distributions are mismatched. In this work, we bound the conditional invalidity of CP under distribution shift in terms of the Wasserstein distance between the calibration and test distributions. This result highlights the role of invertible transport in mitigating conditional coverage degradation. Motivated by this insight, we introduce Branched Normalizing Flow (BNF), a two-branch architecture that normalizes a test input to the calibration distribution and transforms the prediction set of the normalized input back to the test distribution while preserving conditional guarantees. Empirically, BNF consistently improves conditional coverage robustness on nine datasets across a wide range of confidence levels.

Rui Xu, Xingyuan Chen, Wenxing Huang et al.

Conformal Prediction (CP) provides distribution-free uncertainty quantification by constructing prediction sets that guarantee coverage of the true labels. This reliability makes CP valuable for high-stakes federated learning scenarios such as multi-center healthcare. However, standard CP assumes i.i.d. data, which is violated in federated settings where client distributions differ substantially. Existing federated CP methods address this by maintaining marginal coverage on each client, but such guarantees often fail to reflect input-conditional uncertainty. In this work, we propose Federated Conditional Conformal Prediction (Fed-CCP) via generative models, which aims for conditional coverage that adapts to local data heterogeneity. Fed-CCP leverages generative models, such as normalizing flows or diffusion models, to approximate conditional data distributions without requiring the sharing of raw data. This enables each client to locally calibrate conformal scores that reflect its unique uncertainty, while preserving global consistency through federated aggregation. Experiments on real datasets demonstrate that Fed-CCP achieves more adaptive prediction sets.