# Leverage-Weighted Conformal Prediction

arXiv: https://arxiv.org/abs/2602.12693 · HTML: https://mlsanity.com/paper/2602.12693/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [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)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Boosted Conformal Prediction Intervals](https://mlsanity.com/paper/2406.07449/) (2024)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Integrating Uncertainty Awareness into Conformalized Quantile Regression](https://mlsanity.com/paper/2306.08693/) (2023)
- [Adaptive Conformal Prediction by Reweighting Nonconformity Score](https://mlsanity.com/paper/2303.12695/) (2023)
- [Self-Calibrating Conformal Prediction](https://mlsanity.com/paper/2402.07307/) (2024)
- [Efficiency of conformalized ridge regression](https://mlsanity.com/paper/1404.2083/) (2014)
- [Fast Conformal Prediction using Conditional Interquantile Intervals](https://mlsanity.com/paper/2601.02769/) (2026)
- [CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regression](https://mlsanity.com/paper/2512.01384/) (2025)

## Abstract (arXiv)

Split conformal prediction provides distribution-free prediction intervals with finite-sample marginal coverage, but produces constant-width intervals that overcover in low-variance regions and undercover in high-variance regions. Existing adaptive methods require training auxiliary models. We propose Leverage-Weighted Conformal Prediction (LWCP), which weights nonconformity scores by a function of the statistical leverage -- the diagonal of the hat matrix -- deriving adaptivity from the geometry of the design matrix rather than from auxiliary model fitting. We prove that LWCP preserves finite-sample marginal validity for any weight function; achieves asymptotically optimal conditional coverage at essentially no width cost when heteroscedasticity factors through leverage; and recovers the form and width of classical prediction intervals under Gaussian assumptions while retaining distribution-free guarantees. We further establish that randomized leverage approximations preserve coverage exactly with controlled width perturbation, and that vanilla CP suffers a persistent, sample-size-independent conditional coverage gap that LWCP eliminates. The method requires no hyperparameters beyond the choice of weight function and adds negligible computational overhead to vanilla CP. Experiments on synthetic and real data confirm the theoretical predictions, demonstrating substantial reductions in conditional coverage disparity across settings.