# Training-Conditional Coverage Bounds under Covariate Shift

arXiv: https://arxiv.org/abs/2405.16594 · HTML: https://mlsanity.com/paper/2405.16594/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 52 references that are in the map.
- First posted on arXiv 26 May 2024.

## Builds on (most cited first, 17 of 17)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Domain adaptation under structural causal models](https://mlsanity.com/paper/2010.15764/) (2020)
- [Label Noise Robustness of Conformal Prediction](https://mlsanity.com/paper/2209.14295/) (2022)
- [JAWS: Auditing Predictive Uncertainty Under Covariate Shift](https://mlsanity.com/paper/2207.10716/) (2022)
- [Can Pretext-Based Self-Supervised Learning Be Boosted by Downstream Data? A Theoretical Analysis](https://mlsanity.com/paper/2103.03568/) (2021)
- [Spectrally-truncated kernel ridge regression and its free lunch](https://mlsanity.com/paper/1906.06276/) (2019)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Low-Rank Approximation of Structural Redundancy for Self-Supervised Learning](https://mlsanity.com/paper/2402.06884/) (2024)

## Built on by (most cited first, 8 of 8)

- [Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage](https://mlsanity.com/paper/2502.17264/) (2025)
- [Anytime-Valid Conformal Risk Control](https://mlsanity.com/paper/2602.04364/) (2026)
- [Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts](https://mlsanity.com/paper/2605.02072/) (2026)
- [Multi-Agent Conformal Prediction with Personalized Statistical Validity](https://mlsanity.com/paper/2606.00717/) (2026)
- [Sharp training-conditional coverage for conformal prediction under covariate shift](https://mlsanity.com/paper/2609.33456/) (2026)
- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [Conformal PM2.5 Mapping Under Spatial Covariate Shift: Satellite-Reanalysis Fusion for Africa's Green Industrial Transition](https://mlsanity.com/paper/2604.22787/) (2026)

## Abstract (arXiv)

Conformal prediction methodology has recently been extended to the covariate shift setting, where the distribution of covariates differs between training and test data. While existing results ensure that the prediction sets from these methods achieve marginal coverage above a nominal level, their coverage rate conditional on the training dataset (referred to as training-conditional coverage) remains unexplored. In this paper, we address this gap by deriving upper bounds on the tail of the training-conditional coverage distribution, offering probably approximately correct (PAC) guarantees for these methods. Our results characterize the reliability of the prediction sets in terms of the severity of distributional changes and the size of the training dataset.