# Colorful Pinball: Density-Weighted Quantile Regression for Conditional Guarantee of Conformal Prediction

arXiv: https://arxiv.org/abs/2512.24139 · HTML: https://mlsanity.com/paper/2512.24139/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction](https://mlsanity.com/paper/2001.00106/) (2019)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Boosted Conformal Prediction Intervals](https://mlsanity.com/paper/2406.07449/) (2024)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data](https://mlsanity.com/paper/2102.06746/) (2021)
- [Conditional Coverage Diagnostics for Conformal Prediction](https://mlsanity.com/paper/2512.11779/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Correcting the Coverage Bias of Quantile Regression](https://mlsanity.com/paper/2511.00820/) (2025)

## Built on by (most cited first, 3 of 3)

- [Uncertainty-Aware Reward Modeling for Stable RLHF](https://mlsanity.com/paper/2606.19818/) (2026)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [How Synthetic Labels Improve Conformal Prediction: A Perspective on Conditional Coverage](https://mlsanity.com/paper/2609.33482/) (2026)

## Abstract (arXiv)

Although conformal prediction provides robust marginal coverage guarantees, achieving reliable conditional coverage for specific inputs remains challenging. While exact distribution-free conditional coverage is impossible with finite samples, recent work has focused on improving the conditional coverage of standard conformal procedures. Distinct from approaches that target relaxed notions of conditional coverage, we directly target the mean squared error of conditional coverage by refining the quantile regression components that underpin many conformal methods. Leveraging a Taylor expansion, we derive a sharp surrogate objective for quantile regression: a density-weighted pinball loss, where the weights are given by the conditional density of the nonconformity score evaluated at the true quantile. We propose a three-headed quantile network that estimates these weights via finite differences using auxiliary quantile levels at 1-α ± δ, subsequently fine-tuning the central quantile by optimizing the weighted loss. We provide a theoretical analysis with exact non-asymptotic guarantees characterizing the resulting excess risk. Extensive experiments on diverse high-dimensional real-world datasets demonstrate remarkable improvements in conditional coverage performance.