# Online Localized Conformal Prediction

arXiv: https://arxiv.org/abs/2605.05497 · HTML: https://mlsanity.com/paper/2605.05497/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 21 of 21)

- [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)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Temporal Convolutional Networks: A Unified Approach to Action Segmentation](https://mlsanity.com/paper/1608.08242/) (2016)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Follow the Leader If You Can, Hedge If You Must](https://mlsanity.com/paper/1301.0534/) (2013)
- [Second-order Quantile Methods for Experts and Combinatorial Games](https://mlsanity.com/paper/1502.08009/) (2015)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Conformal prediction with local weights: randomization enables local guarantees](https://mlsanity.com/paper/2310.07850/) (2023)
- [Optimal Algorithms for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2310.18955/) (2023)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [Online Conformal Prediction via Universal Portfolio Algorithms](https://mlsanity.com/paper/2602.03168/) (2026)

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

- [Online Conformal Prediction for Non-Exchangeable Panel Data](https://mlsanity.com/paper/2605.17705/) (2026)

## Abstract (arXiv)

Conformal prediction is a framework that provides valid uncertainty quantification for general models with exchangeable data. However, in the online learning and time-series settings, exchangeability is not satisfied. Existing online conformal methods, such as adaptive conformal inference (ACI), can achieve long-run validity, yet they remain inefficient under covariate heterogeneity because they rely on global calibration. We propose Online Localized Conformal Prediction (OLCP), which combines online adaptation with covariate-dependent localization to better reflect heterogeneity. To reduce sensitivity to the localization bandwidth, we further develop OLCP-Hedge, which performs bandwidth selection as an online expert aggregation problem using a constrained online convex optimization framework. Importantly, we provide coverage guarantees for both algorithms and demonstrate through simulations and real-data experiments that the proposed methods attain valid long-run coverage with narrower prediction sets than existing baselines.