Online Localized Conformal Prediction
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911662495236096 |
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| author | Lai, Yuheng Raskutti, Garvesh |
| author_facet | Lai, Yuheng Raskutti, Garvesh |
| contents | 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 \emph{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 \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Online Localized Conformal Prediction Lai, Yuheng Raskutti, Garvesh Machine Learning 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 \emph{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 \emph{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. |
| title | Online Localized Conformal Prediction |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.05497 |