![[2602.12693] Leverage-Weighted Conformal Prediction](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.12693] Leverage-Weighted Conformal Prediction
Summary
The paper introduces Leverage-Weighted Conformal Prediction (LWCP), a method that enhances prediction intervals by adapting to variance without auxiliary models, ensuring finite-sample validity and optimal coverage.
Why It Matters
LWCP addresses limitations in traditional conformal prediction methods, particularly in handling varying data variance. By improving prediction accuracy and reliability, it has significant implications for fields relying on precise statistical predictions, such as finance and healthcare.
Key Takeaways
- LWCP improves prediction intervals by using leverage scores, enhancing adaptivity.
- The method maintains finite-sample validity without needing auxiliary models.
- LWCP achieves optimal conditional coverage with minimal computational overhead.
- Experiments validate the theoretical benefits, showing reduced coverage disparity.
- No hyperparameters are required beyond the choice of weight function.
Computer Science > Machine Learning arXiv:2602.12693 (cs) [Submitted on 13 Feb 2026] Title:Leverage-Weighted Conformal Prediction Authors:Shreyas Fadnavis View a PDF of the paper titled Leverage-Weighted Conformal Prediction, by Shreyas Fadnavis View PDF HTML (experimental) Abstract: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 choic...
