# Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization

arXiv: https://arxiv.org/abs/2502.13030 · HTML: https://mlsanity.com/paper/2502.13030/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 74 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [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)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [RxRx1: A Dataset for Evaluating Experimental Batch Correction Methods](https://mlsanity.com/paper/2301.05768/) (2023)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)

## Built on by (most cited first, 12 of 12)

- [SCOPE: Selective Conformal Optimized Pairwise LLM Judging](https://mlsanity.com/paper/2602.13110/) (2026)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [Singleton-Optimized Conformal Prediction](https://mlsanity.com/paper/2509.24095/) (2025)
- [Non-Asymptotic Analysis of Efficiency in Conformalized Regression](https://mlsanity.com/paper/2510.07093/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)
- [Machine-Learning-Assisted Comparison of Regression Functions](https://mlsanity.com/paper/2510.24714/) (2025)
- [GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs](https://mlsanity.com/paper/2605.08074/) (2026)
- [The Label Complexity of Useful Class-Conditional Prediction Sets under Distribution Shift](https://mlsanity.com/paper/2607.18088/) (2026)
- [CHOIR: heterogeneity-aware conformal prediction for crash injury severity across driver safety strata](https://mlsanity.com/paper/2609.11592/) (2026)
- [Sketched Calibration for Conformal Prediction under Covariate Shift](https://mlsanity.com/paper/2610.09208/) (2026)

## Abstract (arXiv)

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.