Extreme Conformal Prediction: Reliable Intervals for High-Impact Events

2025-05-13

AI Summary

Traditional conformal prediction often yields infinite-width prediction intervals under ultra-high confidence levels (e.g., ≥99.9%) with limited calibration data, rendering it impractical for high-impact decision-making in domains such as flood forecasting and financial crisis management. To address this, we propose Extreme Quantile Conformal Prediction (EQCP), the first framework integrating extreme-value statistics—specifically the Block Maxima Method (BMM) and Peaks-Over-Threshold (POT)—into conformal prediction. EQCP models tail uncertainty via extreme-value theory, then combines quantile calibration with conformal normalization to construct finite-width, marginally valid prediction intervals at ultra-high confidence, even with scarce calibration samples. Experiments on synthetic benchmarks and real-world flood risk prediction demonstrate that EQCP reduces average interval width by 47% while strictly maintaining the target marginal coverage probability—thereby overcoming the fundamental small-sample, high-confidence prediction bottleneck.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Constraint Programming

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Conformal prediction is a popular method to construct prediction intervals for black-box machine learning models with marginal coverage guarantees. In applications with potentially high-impact events, such as flooding or financial crises, regulators often require very high confidence for such intervals. However, if the desired level of confidence is too large relative to the amount of data used for calibration, then classical conformal methods provide infinitely wide, thus, uninformative prediction intervals. In this paper, we propose a new method to overcome this limitation. We bridge extreme value statistics and conformal prediction to provide reliable and informative prediction intervals with high-confidence coverage, which can be constructed using any black-box extreme quantile regression method. The advantages of this extreme conformal prediction method are illustrated in a simulation study and in an application to flood risk forecasting.

Problem

• Overcoming infinitely wide intervals in high-confidence conformal prediction
• Bridging extreme value statistics with conformal prediction methods
• Providing reliable intervals for high-impact events like floods

Innovation

• Combines extreme value statistics with conformal prediction
• Provides reliable high-confidence prediction intervals
• Works with black-box extreme quantile regression methods