Probabilistic Conformal Prediction with Approximate Conditional Validity

Vincent Plassier, Alexander Fishkov, Mohsen Guizani, Maxim Panov, Eric Moulines

Keywords: Conformal Prediction, Conditional coverage, Probabilistic method, Uncertainty Quantification

TL;DR: We introduce a method that effectively integrates conformal approaches with an estimate of the conditional distribution to ensure the approximate conditional validity.

Abstract: We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $\textup{P}_{Y \mid X}$. Existing methods, such as conformalized quantile regression and probabilistic conformal prediction, usually provide only a marginal coverage guarantee. In contrast, our approach extends these frameworks to achieve approximately conditional coverage, which is crucial for many practical applications. Our prediction sets adapt to the behavior of the predictive distribution, making them effective even under high heteroscedasticity. While exact conditional guarantees are infeasible without assumptions on the underlying data distribution, we derive non-asymptotic bounds that depend on the total variation distance of the conditional distribution and its estimate. Using extensive simulations, we show that our method consistently outperforms existing approaches in terms of conditional coverage, leading to more reliable statistical inference in a variety of applications.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 14036