SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals

Ilia Azizi, Marc-Olivier Boldi, Valérie Chavez-Demoulin
Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 266:250-281, 2025.

Abstract

This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals with any ML model. SEMF extends the Expectation-Maximization algorithm, traditionally used in unsupervised learning, to a supervised context, leveraging latent variable modeling for uncertainty estimation. Through extensive empirical evaluation of diverse simulated distributions and 11 real-world tabular datasets, SEMF consistently produces narrower prediction intervals while maintaining the desired coverage probability, outperforming traditional quantile regression methods. Furthermore, without using the quantile (pinball) loss, SEMF allows point predictors, including gradient-boosted trees and neural networks, to be calibrated with conformal quantile regression. The results indicate that SEMF enhances uncertainty quantification under diverse data distributions and is particularly effective for models that otherwise struggle with inherent uncertainty representation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v266-azizi25a, title = {SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals}, author = {Azizi, Ilia and Boldi, Marc-Olivier and Chavez-Demoulin, Val\'{e}rie}, booktitle = {Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {250--281}, 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/azizi25a/azizi25a.pdf}, url = {https://proceedings.mlr.press/v266/azizi25a.html}, abstract = {This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals with any ML model. SEMF extends the Expectation-Maximization algorithm, traditionally used in unsupervised learning, to a supervised context, leveraging latent variable modeling for uncertainty estimation. Through extensive empirical evaluation of diverse simulated distributions and 11 real-world tabular datasets, SEMF consistently produces narrower prediction intervals while maintaining the desired coverage probability, outperforming traditional quantile regression methods. Furthermore, without using the quantile (pinball) loss, SEMF allows point predictors, including gradient-boosted trees and neural networks, to be calibrated with conformal quantile regression. The results indicate that SEMF enhances uncertainty quantification under diverse data distributions and is particularly effective for models that otherwise struggle with inherent uncertainty representation.} }
Endnote
%0 Conference Paper %T SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals %A Ilia Azizi %A Marc-Olivier Boldi %A Valérie Chavez-Demoulin %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-azizi25a %I PMLR %P 250--281 %U https://proceedings.mlr.press/v266/azizi25a.html %V 266 %X This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals with any ML model. SEMF extends the Expectation-Maximization algorithm, traditionally used in unsupervised learning, to a supervised context, leveraging latent variable modeling for uncertainty estimation. Through extensive empirical evaluation of diverse simulated distributions and 11 real-world tabular datasets, SEMF consistently produces narrower prediction intervals while maintaining the desired coverage probability, outperforming traditional quantile regression methods. Furthermore, without using the quantile (pinball) loss, SEMF allows point predictors, including gradient-boosted trees and neural networks, to be calibrated with conformal quantile regression. The results indicate that SEMF enhances uncertainty quantification under diverse data distributions and is particularly effective for models that otherwise struggle with inherent uncertainty representation.
APA
Azizi, I., Boldi, M. & Chavez-Demoulin, V.. (2025). SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals. Proceedings of the Fourteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 266:250-281 Available from https://proceedings.mlr.press/v266/azizi25a.html.

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