Distribution-free possibilistic inference on conditional quantities

Leonardo Cella
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:60-70, 2025.

Abstract

Uncertainty quantification for conditional quantities—i.e., unknown quantities related to the conditional distribution of a response variable given covariates—is a fundamental problem. Existing methods often rely on restrictive parametric assumptions or smoothness conditions and typically only provide set estimates for the unknown quantities. This paper introduces Inferential Models (IMs) that offer possibilistic uncertainty quantification for conditional quantities, going beyond the simple provision of set estimates. Unlike traditional approaches, the proposed IMs are fully distribution-free and can handle both random and fixed conditional quantities. Moreover, they satisfy a marginal validity criterion, ensuring proper calibration of all IMs’ outputs when averaged over the covariates distribution. Illustrations of this framework are provided for both random and fixed conditional quantities—specifically, a future response and the conditional median, respectively.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-cella25a, title = {Distribution-free possibilistic inference on conditional quantities}, author = {Cella, Leonardo}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {60--70}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/cella25a/cella25a.pdf}, url = {https://proceedings.mlr.press/v290/cella25a.html}, abstract = {Uncertainty quantification for conditional quantities—i.e., unknown quantities related to the conditional distribution of a response variable given covariates—is a fundamental problem. Existing methods often rely on restrictive parametric assumptions or smoothness conditions and typically only provide set estimates for the unknown quantities. This paper introduces Inferential Models (IMs) that offer possibilistic uncertainty quantification for conditional quantities, going beyond the simple provision of set estimates. Unlike traditional approaches, the proposed IMs are fully distribution-free and can handle both random and fixed conditional quantities. Moreover, they satisfy a marginal validity criterion, ensuring proper calibration of all IMs’ outputs when averaged over the covariates distribution. Illustrations of this framework are provided for both random and fixed conditional quantities—specifically, a future response and the conditional median, respectively.} }
Endnote
%0 Conference Paper %T Distribution-free possibilistic inference on conditional quantities %A Leonardo Cella %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-cella25a %I PMLR %P 60--70 %U https://proceedings.mlr.press/v290/cella25a.html %V 290 %X Uncertainty quantification for conditional quantities—i.e., unknown quantities related to the conditional distribution of a response variable given covariates—is a fundamental problem. Existing methods often rely on restrictive parametric assumptions or smoothness conditions and typically only provide set estimates for the unknown quantities. This paper introduces Inferential Models (IMs) that offer possibilistic uncertainty quantification for conditional quantities, going beyond the simple provision of set estimates. Unlike traditional approaches, the proposed IMs are fully distribution-free and can handle both random and fixed conditional quantities. Moreover, they satisfy a marginal validity criterion, ensuring proper calibration of all IMs’ outputs when averaged over the covariates distribution. Illustrations of this framework are provided for both random and fixed conditional quantities—specifically, a future response and the conditional median, respectively.
APA
Cella, L.. (2025). Distribution-free possibilistic inference on conditional quantities. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:60-70 Available from https://proceedings.mlr.press/v290/cella25a.html.

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