# Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts

arXiv: https://arxiv.org/abs/2605.02072 · HTML: https://mlsanity.com/paper/2605.02072/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 3 May 2026.

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

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [The iWildCam 2021 Competition Dataset](https://mlsanity.com/paper/2105.03494/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examples](https://mlsanity.com/paper/2007.05145/) (2020)
- [Calibrated Prediction with Covariate Shift via Unsupervised Domain Adaptation](https://mlsanity.com/paper/2003.00343/) (2020)
- [Tight Hardness Results for Training Depth-2 ReLU Networks](https://mlsanity.com/paper/2011.13550/) (2020)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [Practical and Consistent Estimation of f-Divergences](https://mlsanity.com/paper/1905.11112/) (2019)
- [Not all distributional shifts are equal: Fine-grained robust conformal inference](https://mlsanity.com/paper/2402.13042/) (2024)
- [Trimmed Density Ratio Estimation](https://mlsanity.com/paper/1703.03216/) (2017)
- [Efficient Learning with Arbitrary Covariate Shift](https://mlsanity.com/paper/2102.07802/) (2021)
- [Wasserstein-regularized Conformal Prediction under General Distribution Shift](https://mlsanity.com/paper/2501.13430/) (2025)
- [Robust Inference Using Inverse Probability Weighting](https://mlsanity.com/paper/1810.11397/) (2018)
- [Group-Weighted Conformal Prediction](https://mlsanity.com/paper/2401.17452/) (2024)
- [Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data](https://mlsanity.com/paper/2405.15337/) (2024)
- [Training-Conditional Coverage Bounds under Covariate Shift](https://mlsanity.com/paper/2405.16594/) (2024)

## Built on by (most cited first, 4 of 4)

- [Sharp training-conditional coverage for conformal prediction under covariate shift](https://mlsanity.com/paper/2609.33456/) (2026)
- [Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift](https://mlsanity.com/paper/2608.10893/) (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)

Conformal prediction (CP) provides powerful, distribution-free prediction sets, but its guarantees rely on the exchangeability of training and test data, which is often violated in practice due to covariate shifts. While weighted conformal prediction (WCP) is designed to handle such shifts, it can suffer from significant undercoverage when the density ratio between the distributions is unbounded and/or must be learned. This is because of both overfitting in learning the density ratio, and high variance in estimating the nonconformity score threshold. To address this, we introduce clipped least-squares importance fitting (CLISF) as a reduced-variance method for density ratio estimation. Specifically, we show that density ratios learned using CLISF, when plugged into WCP, have bounded expected undercoverage. Furthermore, we show that the undercoverage can be corrected by running WCP with a slightly inflated coverage target; crucially, we are able to estimate the required level of inflation from the data. We provide the first theoretical guarantees for weight clipping in conformal inference, achieving dataset-conditional coverage with a sample complexity that does not blow up with the higher moments of the true density ratio -- a key limitation of prior work. We verify our results on real-world benchmarks and synthetic data.