Error-quantified Conformal Inference for Time Series

TL;DR

This paper introduces Error-quantified Conformal Inference (ECI), a novel method for uncertainty quantification in time series prediction that adaptively incorporates error dynamics for more accurate and tighter prediction sets.

Contribution

ECI is the first conformal inference method to integrate error quantification via smoothing the quantile loss, providing adaptive feedback and long-term coverage guarantees under distribution shifts.

Findings

ECI achieves valid miscoverage control in diverse time series scenarios.

ECI produces tighter prediction sets compared to existing methods.

Experimental results confirm the robustness and effectiveness of ECI.

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 \textit{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.