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In many real-world applications, such as weather forecasting, macroeconomic prediction, and risk management, different users operate under heterogeneous risk tolerances and require calibrated uncertainty estimates across a range of coverage levels. In such setting"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the online optimization framework with small regret directly enforces both the coverage guarantees and the strict nestedness of prediction sets across levels without post-hoc adjustments or loss of efficiency.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Two novel online conformal prediction algorithms enforce nested prediction sets across coverage levels using online optimization with regret bounds for quantile error control.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Online conformal prediction methods produce nested sets across coverage levels by using low-regret online optimization to control quantile errors.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"68e8542d14e8cdb142872e31ae14d98d81dffd16ac6b513d6ec2683fb93fad42"},"source":{"id":"2605.12668","kind":"arxiv","version":1},"verdict":{"id":"6a6d4e71-3afd-4cac-beaf-9e72131e8370","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:02:01.287080Z","strongest_claim":"Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets.","one_line_summary":"Two novel online conformal prediction algorithms enforce nested prediction sets across coverage levels using online optimization with regret bounds for quantile error control.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the online optimization framework with small regret directly enforces both the coverage guarantees and the strict nestedness of prediction sets across levels without post-hoc adjustments or loss of efficiency.","pith_extraction_headline":"Online conformal prediction methods produce nested sets across coverage levels by using low-regret online optimization to control quantile errors."},"references":{"count":29,"sample":[{"doi":"","year":null,"title":"The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=","work_id":"afcf6681-617d-4e87-9635-ff5e4552cb84","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"European conference on machine learning , pages=","work_id":"f691f1cf-e556-4ba0-818d-31916634d675","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Algorithmic learning in a random world , author=. 2005 , publisher=","work_id":"31470f85-2f7f-4117-905b-da888e9ae129","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"A Tutorial on Conformal Prediction. , author=. 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