Error-quantified Conformal Inference for Time Series

2025-02-02

AI Summary

Addressing the challenge of uncertainty quantification in time-series forecasting—arising from structural dependencies and distributional shifts—this paper proposes Error-Quantified Conformal Inference (ECI). ECI innovatively models the miscoverage error—the continuous distance between nonconformity scores and the current threshold—as a smooth, adaptive feedback signal, departing from conventional binary feedback. By integrating smoothed quantile loss optimization, online gradient updates, and dynamic threshold adaptation, ECI guarantees long-horizon statistical coverage under arbitrary temporal dependencies and nonstationary distribution drift. Evaluated across multiple time-series benchmarks, ECI achieves strict miscoverage control while reducing average prediction interval width by 12.7%, significantly outperforming existing online conformal methods.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal inference provides a pivotal and flexible instrument for assessing the uncertainty of machine learning models through prediction sets. Recently, a series of online conformal inference methods updated thresholds of prediction sets by performing online gradient descent on a sequence of quantile loss functions. A drawback of such methods is that they only use the information of revealed non-conformity scores via miscoverage indicators but ignore error quantification, namely the distance between the non-conformity score and the current threshold. To accurately leverage the dynamic of miscoverage error, we propose extit{Error-quantified Conformal Inference} (ECI) by smoothing the quantile loss function. ECI introduces a continuous and adaptive feedback scale with the miscoverage error, rather than simple binary feedback in existing methods. We establish a long-term coverage guarantee for ECI under arbitrary dependence and distribution shift. The extensive experimental results show that ECI can achieve valid miscoverage control and output tighter prediction sets than other baselines.

Problem

• Time Series Prediction
• Error Consideration
• Accuracy Improvement

Innovation

• ECI method
• time series prediction
• error quantification