Online Conformal Model Selection for Nonstationary Time Series
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910003472891904 |
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| author | Li, Shibo Zheng, Yao |
| author_facet | Li, Shibo Zheng, Yao |
| contents | This paper introduces the MPS (Model Prediction Set), a novel framework for online model selection for nonstationary time series. Classical model selection methods, such as information criteria and cross-validation, rely heavily on the stationarity assumption and often fail in dynamic environments which undergo gradual or abrupt changes over time. Yet real-world data are rarely stationary, and model selection under nonstationarity remains a largely open problem. To tackle this challenge, we combine conformal inference with model confidence sets to develop a procedure that adaptively selects models best suited to the evolving dynamics at any given time. Concretely, the MPS updates in real time a confidence set of candidate models that covers the best model for the next time period with a specified long-run probability, while adapting to nonstationarity of unknown forms. Through simulations and real-world data analysis, we demonstrate that MPS reliably and efficiently identifies optimal models under nonstationarity, an essential capability lacking in offline methods. Moreover, MPS frequently produces high-quality sets with small cardinality, whose evolution offers deeper insights into changing dynamics. As a generic framework, MPS accommodates any data-generating process, data structure, model class, training method, and evaluation metric, making it broadly applicable across diverse problem settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Online Conformal Model Selection for Nonstationary Time Series Li, Shibo Zheng, Yao Machine Learning This paper introduces the MPS (Model Prediction Set), a novel framework for online model selection for nonstationary time series. Classical model selection methods, such as information criteria and cross-validation, rely heavily on the stationarity assumption and often fail in dynamic environments which undergo gradual or abrupt changes over time. Yet real-world data are rarely stationary, and model selection under nonstationarity remains a largely open problem. To tackle this challenge, we combine conformal inference with model confidence sets to develop a procedure that adaptively selects models best suited to the evolving dynamics at any given time. Concretely, the MPS updates in real time a confidence set of candidate models that covers the best model for the next time period with a specified long-run probability, while adapting to nonstationarity of unknown forms. Through simulations and real-world data analysis, we demonstrate that MPS reliably and efficiently identifies optimal models under nonstationarity, an essential capability lacking in offline methods. Moreover, MPS frequently produces high-quality sets with small cardinality, whose evolution offers deeper insights into changing dynamics. As a generic framework, MPS accommodates any data-generating process, data structure, model class, training method, and evaluation metric, making it broadly applicable across diverse problem settings. |
| title | Online Conformal Model Selection for Nonstationary Time Series |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.05544 |