# Time-uniform conformal and PAC prediction

arXiv: https://arxiv.org/abs/2602.06297 · HTML: https://mlsanity.com/paper/2602.06297/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Online Learning: A Comprehensive Survey](https://mlsanity.com/paper/1802.02871/) (2018)
- [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)
- [Self-Driving Cars: A Survey](https://mlsanity.com/paper/1901.04407/) (2019)
- [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)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Sequential estimation of quantiles with applications to A/B-testing and best-arm identification](https://mlsanity.com/paper/1906.09712/) (2019)
- [E-Values Expand the Scope of Conformal Prediction](https://mlsanity.com/paper/2503.13050/) (2025)
- [Discounted Online Convex Optimization: Uniform Regret Across a Continuous Interval](https://mlsanity.com/paper/2505.19491/) (2025)

## Built on by (most cited first, 1 of 1)

- [Rolling Conformal Prediction in Sequential Model Training](https://mlsanity.com/paper/2609.26951/) (2026)

## Abstract (arXiv)

Given that machine learning algorithms are increasingly being deployed to aid in high stakes decision-making, uncertainty quantification methods that wrap around these black box models such as conformal prediction have received much attention in recent years. In sequential settings, where data are observed/generated in a streaming fashion, traditional conformal methods do not provide any guarantee without fixing the sample size. More importantly, traditional conformal methods cannot cope with sequentially updated predictions. As such, we develop an extension of the conformal prediction and related probably approximately correct (PAC) prediction frameworks to sequential settings where the number of data points is not fixed in advance. The resulting prediction sets are anytime-valid in that their expected coverage is at the required level at any time chosen by the analyst even if this choice depends on the data. We present theoretical guarantees for our proposed methods and demonstrate their validity and utility on simulated and real datasets.