Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Model
Xiannan Huang, Shuhan Qiu
TL;DR
The paper proposes Feature Fitted Dynamic Confidence Interval (FFDCI), a lightweight online conformal prediction framework for deep time-series forecasting that leverages features from pretrained point-predictors to train a residual quantile model and dynamically adjust interval lengths during deployment. It provides theoretical guarantees: asymptotic coverage at level $1-\alpha$ with a finite-sample bound, and a MACE bound that scales with the quality of the quantile predictor, captured by $\sigma(q^*-\hat{q})$. Empirically, FFDCI achieves valid coverage with shorter intervals across 12 datasets and multiple base models, and ablations highlight the contributions of both adaptive interval-length updates and feature-conditioned quantile estimation. The approach is practical for real-world deployment since it avoids retraining, adapts to distribution shifts, and demonstrates robust per-dimension and per-horizon calibration, with potential impact on uncertainty-aware decision-making in domains like weather, traffic, and energy systems.
Abstract
Time series forecasting is critical for many applications, where deep learning-based point prediction models have demonstrated strong performance. However, in practical scenarios, there is also a need to quantify predictive uncertainty through online confidence intervals. Existing confidence interval modeling approaches building upon these deep point prediction models suffer from key limitations: they either require costly retraining, fail to fully leverage the representational strengths of deep models, or lack theoretical guarantees. To address these gaps, we propose a lightweight conformal prediction method that provides valid coverage and shorter interval lengths without retraining. Our approach leverages features extracted from pre-trained point prediction models to fit a residual predictor and construct confidence intervals, further enhanced by an adaptive coverage control mechanism. Theoretically, we prove that our method achieves asymptotic coverage convergence, with error bounds dependent on the feature quality of the underlying point prediction model. Experiments on 12 datasets demonstrate that our method delivers tighter confidence intervals while maintaining desired coverage rates. Code, model and dataset in \href{https://github.com/xiannanhuang/FFDCI}{Github}