Dynamic Conformal Prediction for Multi-Target Regression: Optimising Informational Efficiency under Joint Validity

Filip Schlembach, Evgueni Smirnov, Mark H. M. Winands
Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 266:193-213, 2025.

Abstract

Inductive conformal prediction equips point regressors with finite-sample prediction sets that provably contain the unknown label with prescribed probability. For multi-target regression, joint coverage across all output dimensions can be guaranteed by combining one-dimensional conformal predictors, one for each output dimension, resulting in an axis-aligned hyperrectangular prediction region. The validity and informational efficiency of these hyperrectangular prediction regions depend on the choice of the targeted error rate for the individual one-dimensional conformal predictors. We cast this choice as an error-budget allocation problem and introduce Dynamic Conformal Prediction for Multi-Target Regression (DCP-MT), a method that finds the budget allocation, which minimises the hyperrectangles’ volumes while retaining joint coverage under exchangeability. Experiments on synthetic and real-world data sets demonstrate that DCP-MT reduces hyperrectangle volumes compared to state-of-the-art methods when nonconformity scores’ correlations across target dimensions are weak or heterogeneous, while maintaining the nominal coverage. The proposed method thus offers a simple, drop-in solution for existing multi-target regression pipelines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v266-schlembach25a, title = {Dynamic Conformal Prediction for Multi-Target Regression: Optimising Informational Efficiency under Joint Validity}, author = {Schlembach, Filip and Smirnov, Evgueni and Winands, Mark H. M.}, booktitle = {Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {193--213}, year = {2025}, editor = {Nguyen, Khuong An and Luo, Zhiyuan and Papadopoulos, Harris and Löfström, Tuwe and Carlsson, Lars and Boström, Henrik}, volume = {266}, series = {Proceedings of Machine Learning Research}, month = {10--12 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v266/main/assets/schlembach25a/schlembach25a.pdf}, url = {https://proceedings.mlr.press/v266/schlembach25a.html}, abstract = {Inductive conformal prediction equips point regressors with finite-sample prediction sets that provably contain the unknown label with prescribed probability. For multi-target regression, joint coverage across all output dimensions can be guaranteed by combining one-dimensional conformal predictors, one for each output dimension, resulting in an axis-aligned hyperrectangular prediction region. The validity and informational efficiency of these hyperrectangular prediction regions depend on the choice of the targeted error rate for the individual one-dimensional conformal predictors. We cast this choice as an error-budget allocation problem and introduce Dynamic Conformal Prediction for Multi-Target Regression (DCP-MT), a method that finds the budget allocation, which minimises the hyperrectangles’ volumes while retaining joint coverage under exchangeability. Experiments on synthetic and real-world data sets demonstrate that DCP-MT reduces hyperrectangle volumes compared to state-of-the-art methods when nonconformity scores’ correlations across target dimensions are weak or heterogeneous, while maintaining the nominal coverage. The proposed method thus offers a simple, drop-in solution for existing multi-target regression pipelines.} }
Endnote
%0 Conference Paper %T Dynamic Conformal Prediction for Multi-Target Regression: Optimising Informational Efficiency under Joint Validity %A Filip Schlembach %A Evgueni Smirnov %A Mark H. M. Winands %B Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2025 %E Khuong An Nguyen %E Zhiyuan Luo %E Harris Papadopoulos %E Tuwe Löfström %E Lars Carlsson %E Henrik Boström %F pmlr-v266-schlembach25a %I PMLR %P 193--213 %U https://proceedings.mlr.press/v266/schlembach25a.html %V 266 %X Inductive conformal prediction equips point regressors with finite-sample prediction sets that provably contain the unknown label with prescribed probability. For multi-target regression, joint coverage across all output dimensions can be guaranteed by combining one-dimensional conformal predictors, one for each output dimension, resulting in an axis-aligned hyperrectangular prediction region. The validity and informational efficiency of these hyperrectangular prediction regions depend on the choice of the targeted error rate for the individual one-dimensional conformal predictors. We cast this choice as an error-budget allocation problem and introduce Dynamic Conformal Prediction for Multi-Target Regression (DCP-MT), a method that finds the budget allocation, which minimises the hyperrectangles’ volumes while retaining joint coverage under exchangeability. Experiments on synthetic and real-world data sets demonstrate that DCP-MT reduces hyperrectangle volumes compared to state-of-the-art methods when nonconformity scores’ correlations across target dimensions are weak or heterogeneous, while maintaining the nominal coverage. The proposed method thus offers a simple, drop-in solution for existing multi-target regression pipelines.
APA
Schlembach, F., Smirnov, E. & Winands, M.H.M.. (2025). Dynamic Conformal Prediction for Multi-Target Regression: Optimising Informational Efficiency under Joint Validity. Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 266:193-213 Available from https://proceedings.mlr.press/v266/schlembach25a.html.

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