Target-Aligned Full Conformal Bayes under Continuous Label Shift

Juyeon Kim, Hyeonsu Lee, Erkhembayar Jadamba, Seungjin Choi, Hyunjin Shin
Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 329:101-132, 2026.

Abstract

Standard Full Conformal Bayes relies on exchangeability between the source observations and the target point. Under continuous label shift, weighting by the oracle label-density ratio transports rank aggregation to the target label distribution and restores target-domain coverage. However, the posterior predictive that defines the ranks may still reflect source-domain geometry, which can reduce interval efficiency. We propose Target-Aligned Full Conformal Bayes (TA-FCB), which keeps the weighted rank aggregation and additionally tilts each candidate-augmented posterior predictive before the scores are computed. For Bayesian ridge regression, candidate augmentation is a rank-one posterior update, and under an exponential label tilt the predictive tilt is a variance-scaled mean shift. Consequently, the procedure admits a closed-form implementation without candidate-wise refitting. The unrestricted oracle construction has finite-sample target-domain coverage under permutation-symmetric scoring, and the experiments use a shared finite-grid implementation. On two molecular property benchmarks, weighting recovers the coverage lost to controlled label shift, and candidate-wise tilting shortens intervals relative to weighting alone at comparable coverage. Estimated-ratio variants are evaluated separately and are not covered by the finite-sample guarantee.

Cite this Paper

BibTeX
@InProceedings{pmlr-v329-kim26a, title = {Target-Aligned Full Conformal Bayes under Continuous Label Shift}, author = {Kim, Juyeon and Lee, Hyeonsu and Jadamba, Erkhembayar and Choi, Seungjin and Shin, Hyunjin}, booktitle = {Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {101--132}, year = {2026}, editor = {Ahlberg, Ernst and Johansson, Ulf and Boström, Henrik and Carlevaro, Alberto and Hallberg Szabadváry, Johan and Carlsson, Lars}, volume = {329}, series = {Proceedings of Machine Learning Research}, month = {02--04 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v329/main/assets/kim26a/kim26a.pdf}, url = {https://proceedings.mlr.press/v329/kim26a.html}, abstract = {Standard Full Conformal Bayes relies on exchangeability between the source observations and the target point. Under continuous label shift, weighting by the oracle label-density ratio transports rank aggregation to the target label distribution and restores target-domain coverage. However, the posterior predictive that defines the ranks may still reflect source-domain geometry, which can reduce interval efficiency. We propose Target-Aligned Full Conformal Bayes (TA-FCB), which keeps the weighted rank aggregation and additionally tilts each candidate-augmented posterior predictive before the scores are computed. For Bayesian ridge regression, candidate augmentation is a rank-one posterior update, and under an exponential label tilt the predictive tilt is a variance-scaled mean shift. Consequently, the procedure admits a closed-form implementation without candidate-wise refitting. The unrestricted oracle construction has finite-sample target-domain coverage under permutation-symmetric scoring, and the experiments use a shared finite-grid implementation. On two molecular property benchmarks, weighting recovers the coverage lost to controlled label shift, and candidate-wise tilting shortens intervals relative to weighting alone at comparable coverage. Estimated-ratio variants are evaluated separately and are not covered by the finite-sample guarantee.} }
Endnote
%0 Conference Paper %T Target-Aligned Full Conformal Bayes under Continuous Label Shift %A Juyeon Kim %A Hyeonsu Lee %A Erkhembayar Jadamba %A Seungjin Choi %A Hyunjin Shin %B Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2026 %E Ernst Ahlberg %E Ulf Johansson %E Henrik Boström %E Alberto Carlevaro %E Johan Hallberg Szabadváry %E Lars Carlsson %F pmlr-v329-kim26a %I PMLR %P 101--132 %U https://proceedings.mlr.press/v329/kim26a.html %V 329 %X Standard Full Conformal Bayes relies on exchangeability between the source observations and the target point. Under continuous label shift, weighting by the oracle label-density ratio transports rank aggregation to the target label distribution and restores target-domain coverage. However, the posterior predictive that defines the ranks may still reflect source-domain geometry, which can reduce interval efficiency. We propose Target-Aligned Full Conformal Bayes (TA-FCB), which keeps the weighted rank aggregation and additionally tilts each candidate-augmented posterior predictive before the scores are computed. For Bayesian ridge regression, candidate augmentation is a rank-one posterior update, and under an exponential label tilt the predictive tilt is a variance-scaled mean shift. Consequently, the procedure admits a closed-form implementation without candidate-wise refitting. The unrestricted oracle construction has finite-sample target-domain coverage under permutation-symmetric scoring, and the experiments use a shared finite-grid implementation. On two molecular property benchmarks, weighting recovers the coverage lost to controlled label shift, and candidate-wise tilting shortens intervals relative to weighting alone at comparable coverage. Estimated-ratio variants are evaluated separately and are not covered by the finite-sample guarantee.
APA
Kim, J., Lee, H., Jadamba, E., Choi, S. & Shin, H.. (2026). Target-Aligned Full Conformal Bayes under Continuous Label Shift. Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 329:101-132 Available from https://proceedings.mlr.press/v329/kim26a.html.

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