A Gibbs-Boltzmann Approach to Conformal Prediction under Distribution Shift

Shivaprasad Channapura Sudhakara, Ilia Nouretdinov
Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 329:1070-1072, 2026.

Abstract

Building on the foundation of standard Conformal Prediction and its known vulnerabilities to covariate shift, we formalize our Thermodynamic DRO framework. While recent methods such as Aolaritei et al. (2025) address score shift via topological metrics like the Lévy-Prokhorov distance, our approach introduces a statistical mechanics perspective. By applying a physics-inspired thermodynamic base measure directly to 1D non-conformity scores within a KL-divergence ambiguity set, we yield a smooth, closed-form partition function that expands conformal thresholds to absorb out-of-distribution errors with minimal computational overhead.

Cite this Paper

BibTeX
@InProceedings{pmlr-v329-channapura-sudhakara26a, title = {A Gibbs-Boltzmann Approach to Conformal Prediction under Distribution Shift}, author = {Channapura Sudhakara, Shivaprasad and Nouretdinov, Ilia}, booktitle = {Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {1070--1072}, 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/channapura-sudhakara26a/channapura-sudhakara26a.pdf}, url = {https://proceedings.mlr.press/v329/channapura-sudhakara26a.html}, abstract = {Building on the foundation of standard Conformal Prediction and its known vulnerabilities to covariate shift, we formalize our Thermodynamic DRO framework. While recent methods such as Aolaritei et al. (2025) address score shift via topological metrics like the Lévy-Prokhorov distance, our approach introduces a statistical mechanics perspective. By applying a physics-inspired thermodynamic base measure directly to 1D non-conformity scores within a KL-divergence ambiguity set, we yield a smooth, closed-form partition function that expands conformal thresholds to absorb out-of-distribution errors with minimal computational overhead.} }
Endnote
%0 Conference Paper %T A Gibbs-Boltzmann Approach to Conformal Prediction under Distribution Shift %A Shivaprasad Channapura Sudhakara %A Ilia Nouretdinov %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-channapura-sudhakara26a %I PMLR %P 1070--1072 %U https://proceedings.mlr.press/v329/channapura-sudhakara26a.html %V 329 %X Building on the foundation of standard Conformal Prediction and its known vulnerabilities to covariate shift, we formalize our Thermodynamic DRO framework. While recent methods such as Aolaritei et al. (2025) address score shift via topological metrics like the Lévy-Prokhorov distance, our approach introduces a statistical mechanics perspective. By applying a physics-inspired thermodynamic base measure directly to 1D non-conformity scores within a KL-divergence ambiguity set, we yield a smooth, closed-form partition function that expands conformal thresholds to absorb out-of-distribution errors with minimal computational overhead.
APA
Channapura Sudhakara, S. & Nouretdinov, I.. (2026). A Gibbs-Boltzmann Approach to Conformal Prediction under Distribution Shift. Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 329:1070-1072 Available from https://proceedings.mlr.press/v329/channapura-sudhakara26a.html.

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