Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference

2024-06-21

arXiv.org

AI Summary

To address the challenge in time-series forecasting of simultaneously guaranteeing theoretical coverage validity and adaptively calibrating prediction interval widths to local prediction difficulty, this paper proposes a novel method integrating heteroscedastic quantile regression (HQR) with width-adaptive conformal inference (WACI). Within the conformal prediction framework, our approach is the first to decouple uncertainty modeling from dynamic width adjustment: HQR explicitly captures heteroscedasticity tied to prediction difficulty, while WACI leverages this heteroscedastic estimate to perform coverage-guaranteed, difficulty-aware interval scaling. Experiments on synthetic and real-world electricity price datasets demonstrate that the method consistently achieves the nominal coverage level, produces intervals whose widths reliably reflect local difficulty, and outperforms state-of-the-art baselines—thereby offering both theoretical rigor and practical efficacy.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

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

Abstract

Constructing prediction intervals for time series forecasting is challenging, particularly when practitioners rely solely on point forecasts. While previous research has focused on creating increasingly efficient intervals, we argue that standard measures alone are inadequate. Beyond efficiency, prediction intervals must adapt their width based on the difficulty of the prediction while preserving coverage regardless of complexity. To address these issues, we propose combining Heteroscedastic Quantile Regression (HQR) with Width-Adaptive Conformal Inference (WACI). This integrated procedure guarantees theoretical coverage and enables interval widths to vary with predictive uncertainty. We assess its performance using both a synthetic example and a real world Electricity Price Forecasting scenario. Our results show that this combined approach meets or surpasses typical benchmarks for validity and efficiency, while also fulfilling important yet often overlooked practical requirements.

Problem

• Adaptive Prediction Interval
• Time Series Forecasting
• Reliability

Innovation

• HQR (Hierarchical Quantile Regression)
• WACI (Width-Adaptive Consistency Inference)
• Adaptive Prediction Intervals