# Conformal Prediction under Exponential-Tilt Joint Shift

arXiv: https://arxiv.org/abs/2609.30886 · HTML: https://mlsanity.com/paper/2609.30886/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [PAC Prediction Sets Under Label Shift](https://mlsanity.com/paper/2310.12964/) (2023)
- [Not all distributional shifts are equal: Fine-grained robust conformal inference](https://mlsanity.com/paper/2402.13042/) (2024)
- [Understanding new tasks through the lens of training data via exponential tilting](https://mlsanity.com/paper/2205.13577/) (2022)
- [Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation](https://mlsanity.com/paper/2606.11865/) (2026)
- [Conformal Bayes for Two-Sided Censored Gaussian Regression under Label Shift](https://mlsanity.com/paper/2607.02173/) (2026)
- [Conformal Prediction for Molecular Properties under Label Shift](https://mlsanity.com/paper/2608.17678/) (2026)
- [Distribution-Free Prediction Sets for Regression under Target Shift](https://mlsanity.com/paper/2510.10985/) (2025)

## Abstract (arXiv)

Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExTRA), introduced for classification by Maity et al. (2023), to estimate structured distribution shifts. We compare using its estimated weights in conformal calibration with additionally tilting the source predictive distribution. Shared learned predictors, estimated weights, calibration samples, and test observations isolate the effect of tilting. Existing theory gives both procedures target coverage with true weights and a common coverage bound with estimated weights. Identification calculations and an analysis of how scoring interacts with weight estimation error help explain why their performance can nevertheless differ. In a synthetic regression setting where the assumed models match the data-generating process and target inputs are informative about the shift, tilting reduces mean set length by about 30% relative to weighting alone, with both methods attaining coverage near nominal. Tilting can instead cause substantial coverage losses in synthetic classification and in regression when target inputs provide little information about the response shift. Real-data experiments also show no consistent benefit. Good coverage from weighted calibration alone does not ensure that adding predictive tilting will preserve coverage. Deciding when to apply this additional adjustment using only source labels and target inputs remains an open problem.