{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bellman-conformal-inference-calibrating","title":"Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series","arxiv_id":"2402.05203","date":"2024-02-07","proceeding":null,"authors":["Zitong Yang","Emmanuel Candès","Lihua Lei"],"abstract":"We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides approximately calibrated prediction intervals. Unlike existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. We find empirically that BCI avoids uninformative intervals that have infinite lengths and generates substantially shorter prediction intervals in multiple applications when compared with existing methods.","url_abs":"https://arxiv.org/abs/2402.05203v2","url_pdf":"https://arxiv.org/pdf/2402.05203v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bellman-conformal-inference-calibrating","repo_url":"https://github.com/zitongyang/bellman-conformal-inference","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"prediction-intervals","task_name":"Prediction Intervals"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series-forecasting","task_name":"Time Series Forecasting"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.05203","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.05203"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/zitongyang/bellman-conformal-inference","reach":{"status":"ok"}}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"56b84caa09feabf3","entry":"preprocess","repo":"zitongyang/bellman-conformal-inference","repo_kind":"official","path":"dataloader/vlfc.py","file_url":"https://github.com/zitongyang/bellman-conformal-inference/blob/HEAD/dataloader/vlfc.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"56b84caa09feabf3"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}