{"paper":{"title":"How fast can you find a good hypothesis?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Anders Aamand, Justin Y. Chen, Maryam Aliakbarpour, Sandeep Silwal","submitted_at":"2025-09-03T21:44:48Z","abstract_excerpt":"In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\\mathcal{H} = \\{H_1, \\ldots, H_n\\}$, and samples from an unknown distribution $P$, both over a domain $\\mathcal{X}$. The goal is to output a distribution $Q$ whose distance to $P$ is comparable to that of the nearest hypothesis in $\\mathcal{H}$. Specifically, if the minimum distance is $\\mathsf{OPT}$, we aim to output $Q$ such that, with probability at least $1-\\delta$, its total variation distance to $P$ is at most $C \\cdot \\mathsf{OPT} + \\varepsilon$. The optimal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.03734","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.03734/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}