Improving Backward Conformal Prediction via Non-Conformity Score Transformation

Junxian Liu, Hao Zeng, Hongxin Wei
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:79675-79700, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-liu26fu, title = {Improving Backward Conformal Prediction via Non-Conformity Score Transformation}, author = {Liu, Junxian and Zeng, Hao and Wei, Hongxin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {79675--79700}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/liu26fu/liu26fu.pdf}, url = {https://proceedings.mlr.press/v306/liu26fu.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Improving Backward Conformal Prediction via Non-Conformity Score Transformation %A Junxian Liu %A Hao Zeng %A Hongxin Wei %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-liu26fu %I PMLR %P 79675--79700 %U https://proceedings.mlr.press/v306/liu26fu.html %V 306 %X 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.
APA
Liu, J., Zeng, H. & Wei, H.. (2026). Improving Backward Conformal Prediction via Non-Conformity Score Transformation. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:79675-79700 Available from https://proceedings.mlr.press/v306/liu26fu.html.

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