# Conformal PID Control for Time Series Prediction

arXiv: https://arxiv.org/abs/2307.16895 · HTML: https://mlsanity.com/paper/2307.16895/

## Key facts

- Cited by 88 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States](https://mlsanity.com/paper/2201.12387/) (2022)

## Built on by (most cited first, 30 of 88)

- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Localized Adaptive Risk Control](https://mlsanity.com/paper/2405.07976/) (2024)
- [Automatically Adaptive Conformal Risk Control](https://mlsanity.com/paper/2406.17819/) (2024)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Conformal online model aggregation](https://mlsanity.com/paper/2403.15527/) (2024)
- [Conformalized Interactive Imitation Learning: Handling Expert Shift and Intermittent Feedback](https://mlsanity.com/paper/2410.08852/) (2024)
- [Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering](https://mlsanity.com/paper/2410.01660/) (2024)
- [Stochastic Online Conformal Prediction with Semi-Bandit Feedback](https://mlsanity.com/paper/2405.13268/) (2024)
- [Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2401.04612/) (2024)
- [Mirror Online Conformal Prediction with Intermittent Feedback](https://mlsanity.com/paper/2503.10345/) (2025)
- [Human-AI Collaborative Uncertainty Quantification](https://mlsanity.com/paper/2510.23476/) (2025)
- [When to Trust the Cheap Check: Weak and Strong Verification for Reasoning](https://mlsanity.com/paper/2602.17633/) (2026)
- [Conformal Policy Learning for Sensorimotor Control Under Distribution Shifts](https://mlsanity.com/paper/2311.01457/) (2023)
- [Adapting Prediction Sets to Distribution Shifts Without Labels](https://mlsanity.com/paper/2406.01416/) (2024)
- [Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints](https://mlsanity.com/paper/2409.07902/) (2024)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [TS-LIF: A Temporal Segment Spiking Neuron Network for Time Series Forecasting](https://mlsanity.com/paper/2503.05108/) (2025)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [CUQDS: Conformal Uncertainty Quantification under Distribution Shift for Trajectory Prediction](https://mlsanity.com/paper/2406.12100/) (2024)
- [CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimators](https://mlsanity.com/paper/2407.06141/) (2024)
- [Online Conformal Prediction with Efficiency Guarantees](https://mlsanity.com/paper/2507.02496/) (2025)

## Abstract (arXiv)

We study the problem of uncertainty quantification for time series prediction, with the goal of providing easy-to-use algorithms with formal guarantees. The algorithms we present build upon ideas from conformal prediction and control theory, are able to prospectively model conformal scores in an online setting, and adapt to the presence of systematic errors due to seasonality, trends, and general distribution shifts. Our theory both simplifies and strengthens existing analyses in online conformal prediction. Experiments on 4-week-ahead forecasting of statewide COVID-19 death counts in the U.S. show an improvement in coverage over the ensemble forecaster used in official CDC communications. We also run experiments on predicting electricity demand, market returns, and temperature using autoregressive, Theta, Prophet, and Transformer models. We provide an extendable codebase for testing our methods and for the integration of new algorithms, data sets, and forecasting rules.