# Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Model

arXiv: https://arxiv.org/abs/2505.08158 · HTML: https://mlsanity.com/paper/2505.08158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 30 of 39)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)

## Abstract (arXiv)

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 hrefhttps://github.com/xiannanhuang/FFDCIGithub