{"paper":{"title":"Bayesian online learning in the one-pass regime: Frequentist validity and uncertainty quantification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Bayesian algorithm for one-pass online learning achieves optimal posterior convergence and an online Bernstein-von Mises theorem.","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Dongguen Kim, Jeyong Lee, Junhyeok Choi, Minwoo Chae","submitted_at":"2026-04-30T05:29:06Z","abstract_excerpt":"Bayesian online learning provides a coherent framework for sequential inference. However, its theoretical understanding remains limited, particularly in the one-pass setting. Existing theoretical guarantees typically require the mini-batch sample size to diverge, a condition that fails in the one-pass regime. In this paper, we propose a new Bayesian online learning algorithm tailored to the one-pass setting, which incorporates a warm-start phase to ensure stable sequential updates. For this algorithm, we show that the sequentially updated posterior attains the optimal convergence rate. Buildin"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For this algorithm, we show that the sequentially updated posterior attains the optimal convergence rate. Building on this, we establish an online analogue of the Bernstein-von Mises theorem, which guarantees valid uncertainty quantification without diverging mini-batch sample sizes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes that a warm-start phase can be incorporated to ensure stable sequential updates in the one-pass regime without violating the single-pass constraint or requiring additional conditions that may not hold for general data streams.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A one-pass Bayesian online learner with warm-start achieves optimal posterior convergence and satisfies an online Bernstein-von Mises theorem for uncertainty quantification.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Bayesian algorithm for one-pass online learning achieves optimal posterior convergence and an online Bernstein-von Mises theorem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3868beb3161d7d79e5dc55114aeb31a75550dedb80d17bf35117cb471f4d951c"},"source":{"id":"2604.27442","kind":"arxiv","version":2},"verdict":{"id":"749f3fdd-a492-46ea-acbd-c9997c88b67d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T09:30:33.058261Z","strongest_claim":"For this algorithm, we show that the sequentially updated posterior attains the optimal convergence rate. Building on this, we establish an online analogue of the Bernstein-von Mises theorem, which guarantees valid uncertainty quantification without diverging mini-batch sample sizes.","one_line_summary":"A one-pass Bayesian online learner with warm-start achieves optimal posterior convergence and satisfies an online Bernstein-von Mises theorem for uncertainty quantification.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes that a warm-start phase can be incorporated to ensure stable sequential updates in the one-pass regime without violating the single-pass constraint or requiring additional conditions that may not hold for general data streams.","pith_extraction_headline":"A Bayesian algorithm for one-pass online learning achieves optimal posterior convergence and an online Bernstein-von Mises theorem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.27442/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T22:36:20.026917Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:15:21.381726Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"76b857ecaa62c06bb110e88e5a8403c7d73d6678699a61c9d3936bda54a4f061"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}