Fast Conformal Prediction using Conditional Interquantile Intervals

2026-01-06

AI Summary

This work addresses the instability in coverage and computational inefficiency of existing distributional conformal prediction methods when handling skewed distributions. We propose Conformal Interquantile Regression (CIR) and its enhanced variant CIR+, which leverage black-box models to estimate quantile intervals and incorporate an interquartile-range-based interval selection mechanism to efficiently construct compact prediction intervals with approximate conditional coverage guarantees. CIR+ further introduces a width selection rule that substantially narrows interval width while preserving coverage. By integrating quantile regression, conformal prediction, and conditional coverage theory—while avoiding conventional histogram construction—our approach achieves an optimal balance between accuracy and efficiency on both synthetic and real-world datasets, outperforming current state-of-the-art methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models to estimate outcome distributions through interquantile ranges, transforming these estimates into compact prediction intervals while achieving approximate conditional coverage. We further propose CIR+ (Conditional Interquantile Regression with More Comparison), which enhances CIR by incorporating a width-based selection rule for interquantile intervals. This refinement yields narrower prediction intervals while maintaining comparable coverage, though at the cost of slightly increased computational time. Both methods address key limitations of existing distributional conformal prediction approaches: they handle skewed distributions more effectively than Conformalized Quantile Regression, and they achieve substantially higher computational efficiency than Conformal Histogram Regression by eliminating the need for histogram construction. Extensive experiments on synthetic and real-world datasets demonstrate that our methods optimally balance predictive accuracy and computational efficiency compared to existing approaches.

Problem

• Conformal Prediction
• Prediction Intervals
• Conditional Coverage
• Skewed Distributions
• Computational Efficiency

Innovation

• Conformal Prediction
• Interquantile Regression
• Conditional Coverage
• Prediction Intervals
• Computational Efficiency