# Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data

arXiv: https://arxiv.org/abs/1802.06300 · HTML: https://mlsanity.com/paper/1802.06300/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2018.

## Built on by (most cited first, 30 of 66)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [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)
- [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)
- [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)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [Recommendation Systems with Distribution-Free Reliability Guarantees](https://mlsanity.com/paper/2207.01609/) (2022)
- [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 Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Conformal online model aggregation](https://mlsanity.com/paper/2403.15527/) (2024)
- [PAC-Wrap: Semi-Supervised PAC Anomaly Detection](https://mlsanity.com/paper/2205.10798/) (2022)
- [Towards Modeling Uncertainties of Self-explaining Neural Networks via Conformal Prediction](https://mlsanity.com/paper/2401.01549/) (2024)
- [Predictive inference for time series: why is split conformal effective despite temporal dependence?](https://mlsanity.com/paper/2510.02471/) (2025)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [Root-finding Approaches for Computing Conformal Prediction Set](https://mlsanity.com/paper/2104.06648/) (2021)

## Abstract (arXiv)

We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As a result, the proposed method retains the exact, model-free validity when the data are i.i.d. or more generally exchangeable, similar to usual conformal inference methods. When exchangeability fails, as is the case for common time series data, the proposed approach is approximately valid under weak assumptions on the conformity score.