Expectation Consistency Loss: Rethink Confidence Calibration under Covariate Shift

Conformal prediction converts point predictions into set-valued predictions with coverage guarantees under exchangeability between calibration and deployment data. We study conformal calibration transfer, where this requirement fails because labeled calibration is available only in a source space, while prediction sets are needed in a target space linked to the source through unlabeled paired observations (e.g., paired modalities or sensor changes). We propose Transported Conformal Calibration (TCC): we transport labeled source calibration into the target space using the paired data, and then correct residual post-transport mismatch using only unlabeled target inputs. We instantiate this correction with two complementary methods: TCC-KS, which uses a label-free uncertainty surrogate to detect mismatch and adjust calibration conservatively, and weighted-TCC, which reweights transported calibration toward the target domain for improved efficiency when weights are stable. We provide finite-sample target-domain coverage guarantees that adapt to an observable measure of mismatch. Across CIFAR-100-C, Tiny-ImageNet-C, and SEN12MS, we show reliable target-domain coverage transfer without labeled target calibration data, with label-free diagnostics that predict when correction is needed.

In high-stakes applications, reliable confidence estimates are as important as the predictions themselves. Confidence calibration ensures that predicted probabilities reflect the likelihood of correctness, making it essential for safe deployment of deep learning models. However, existing methods typically assume access to clean validation data, which is often unrealistic due to label noise and domain shifts. This thesis develops methods for improving calibration under these conditions. First, we address calibration under label noise. Standard methods can produce misleading confidence estimates when labels are unreliable. We propose a framework that uses an estimated noise model to reconstruct noise-free confidence estimates by modeling the relationship between noisy and clean label distributions. We extend this approach to Conformal Prediction (CP), which provides set-valued predictions with guaranteed coverage. Our noise-aware CP method estimates clean conformity scores despite label noise, enabling reliable uncertainty quantification. Next, we study calibration in unsupervised domain adaptation, where a model trained on a labeled source domain is adapted to an unlabeled target domain. Since labeled target data are unavailable, we estimate target-domain accuracy from source performance and domain discrepancies, enabling calibration without target labels. We also consider privacy-preserving settings in which user labels and model outputs must remain protected. We propose a locally differentially private conformal prediction framework that provides valid uncertainty quantification while maintaining privacy guarantees and balancing privacy, computational feasibility, and prediction reliability. Our results bridge calibration theory and practical deployment in safety-critical applications, contributing to reliable, privacy-preserving, and noise-resilient neural network predictions.

Conformal Bayes combines Bayesian posterior predictives with conformal calibration to produce prediction sets that are both statistically valid and geometrically efficient. We study conformal Bayes under label shift from a unified perspective, identifying two complementary approaches that restore nominal target-domain coverage through importance-weighted conformal calibration but operate through independent mechanisms. \emph{Post-hoc calibration} tilts the posterior predictive toward the target domain and corrects the conformal threshold via an importance-weighted quantile, leaving the parameter posterior unchanged. \emph{In-training adaptation} tilts the parameter posterior itself to the target domain, producing a corrected predictive whose highest predictive density region serves as the highest predictive density (HPD)-based prediction set under the fitted target predictive; efficiency is model-dependent and does not imply finite-sample conditional optimality. Two controlled experiments isolate the regime-dependence of each strategy: in the low-dimensional, well-estimated regime StrategyA produces the narrowest valid intervals, while in the high-dimensional, underdetermined regime StrategyB achieves up to $43\%$ width reduction at unchanged coverage, under the stated source-sampling and label-shift assumptions.