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

• URL: http://arxiv.org/abs/2512.24139v2
• Date: Sun, 04 Jan 2026 03:50:59 GMT
• Title: Colorful Pinball: Density-Weighted Quantile Regression for Conditional Guarantee of Conformal Prediction
• Authors: Qianyi Chen, Bo Li,
• Abstract summary: We refine the quantile regression components that underpin many conformal methods.<n>We provide a theoretical analysis with exact non-asymptotic guarantees characterizing the resulting excess risk.<n>Experiments on diverse high-dimensional real-world datasets demonstrate remarkable improvements in conditional coverage performance.
• Score: 7.273442425568326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While conformal prediction provides robust marginal coverage guarantees, achieving reliable conditional coverage for specific inputs remains challenging. Although 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 minimize 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 conformity 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 \(1-α\pm δ\), 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.

Related papers

• Conditional Coverage Diagnostics for Conformal Prediction [47.93989136542648]
  We show that conditional coverage estimation can be a classification problem.<n>We call the resulting family of metrics excess risk of the target coverage (ERT)<n>We release an open-source package for ERT as well as previous conditional coverage metrics.
  arXiv  Detail & Related papers  (2025-12-12T18:47:39Z)
• COIN: Uncertainty-Guarding Selective Question Answering for Foundation Models with Provable Risk Guarantees [51.5976496056012]
  COIN is an uncertainty-guarding selection framework that calibrates statistically valid thresholds to filter a single generated answer per question.<n>COIN estimates the empirical error rate on a calibration set and applies confidence interval methods to establish a high-probability upper bound on the true error rate.<n>We demonstrate COIN's robustness in risk control, strong test-time power in retaining admissible answers, and predictive efficiency under limited calibration data.
  arXiv  Detail & Related papers  (2025-06-25T07:04:49Z)
• Rectifying Conformity Scores for Better Conditional Coverage [75.73184036344908]
  We present a new method for generating confidence sets within the split conformal prediction framework.<n>Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage.
  arXiv  Detail & Related papers  (2025-02-22T19:54:14Z)
• Conformal Prediction Sets with Improved Conditional Coverage using Trust Scores [52.92618442300405]
  It is impossible to achieve exact, distribution-free conditional coverage in finite samples.<n>We propose an alternative conformal prediction algorithm that targets coverage where it matters most.
  arXiv  Detail & Related papers  (2025-01-17T12:01:56Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Conformal Prediction with Missing Values [19.18178194789968]
  We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk.
  arXiv  Detail & Related papers  (2023-06-05T09:28:03Z)
• Adaptive Conformal Prediction by Reweighting Nonconformity Score [0.0]
  We use a Quantile Regression Forest (QRF) to learn the distribution of nonconformity scores and utilize the QRF's weights to assign more importance to samples with residuals similar to the test point. Our approach enjoys an assumption-free finite sample marginal and training-conditional coverage, and under suitable assumptions, it also ensures conditional coverage.
  arXiv  Detail & Related papers  (2023-03-22T16:42:19Z)
• Approximate Conditional Coverage via Neural Model Approximations [0.030458514384586396]
  We analyze a data-driven procedure for obtaining empirically reliable approximate conditional coverage. We demonstrate the potential for substantial (and otherwise unknowable) under-coverage with split-conformal alternatives with marginal coverage guarantees.
  arXiv  Detail & Related papers  (2022-05-28T02:59:05Z)
• Improving Conditional Coverage via Orthogonal Quantile Regression [12.826754199680472]
  We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space. We modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. We empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics.
  arXiv  Detail & Related papers  (2021-06-01T11:02:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.