# Conformal Bayes for Two-Sided Censored Gaussian Regression under Label Shift

arXiv: https://arxiv.org/abs/2607.02173 · HTML: https://mlsanity.com/paper/2607.02173/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [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)
- [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)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Conformalized survival analysis with adaptive cutoffs](https://mlsanity.com/paper/2211.01227/) (2022)
- [Doubly Robust Conformalized Survival Analysis with Right-Censored Data](https://mlsanity.com/paper/2412.09729/) (2024)
- [Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation](https://mlsanity.com/paper/2606.11865/) (2026)

## Built on by (most cited first, 2 of 2)

- [Conformal Bayes under Continuous Label Shift: Sensitivity Analysis and the Limits of Exact Validity](https://mlsanity.com/paper/2609.27976/) (2026)
- [Conformal Prediction under Exponential-Tilt Joint Shift](https://mlsanity.com/paper/2609.30886/) (2026)

## Abstract (arXiv)

Prediction under label shift becomes nonstandard when responses are censored. In a two-sided censored Gaussian model, latent values below L and above U are recorded at the boundary values, so the observed predictive distribution is mixed, with atoms at L and U and a continuous density on (L,U). In this paper we develop conformal Bayes for this mixed-space setting by combining posterior predictive tilting with weighted conformal calibration. Under a two-sided Tobit Gaussian Bayesian prediction head with a Laplace posterior approximation, the tilted predictive distribution has left-atom, interior, and right-atom components, with a three-term closed-form normalizer. The resulting prediction set is a mixed highest density region that can combine boundary atoms with an interior interval and can reduce to atom-only sets under strong censoring. The main technical issue is that latent label shift does not directly give an ordinary density ratio on the observed censored scale. A latent exponential tilt induces tail-averaged atom weights at the censored boundaries, while the interior ratio remains density based. This yields a mixed observed-space calibration weight with two atom ratios and one interior density ratio. The weight corrects the calibration measure, while predictive tilting gives target-adapted mixed-HDR geometry. Synthetic experiments show that weighted tilted conformal Bayes restores marginal coverage with smaller sets than weighted source-score calibration, while revealing a trade-off between marginal coverage and component-wise behavior across atoms and interior observations.