{"paper":{"title":"Batch learning equals online learning in Bayesian supervised learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"H\\^ong V\\^an L\\^e","submitted_at":"2025-10-19T15:39:47Z","abstract_excerpt":"In this paper we study Bayesian supervised learning models proposed by L\\^e in \\cite{Le2025}. We show the existence of Bayesian inversions on universal Bayesian supervised learning models $(\\mathcal{P}(\\mathcal{Y})^{\\mathcal{X}}, \\mu, \\mathrm{Id}_{\\mathcal{P}(\\mathcal{Y})^{\\mathcal{X}}}, \\mathcal{P}(\\mathcal{Y})^{\\mathcal{X}}$ for arbitrary input space $\\mathcal{X}$, Souslin label space $\\mathcal{Y}$, and prior probability measure $\\mu \\in \\mathcal{P}( \\mathcal{P}(\\mathcal{Y})^{\\mathcal{X}})$. Using functoriality of probabilistic morphisms, we prove that sequential and batch Bayesian inversion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16892","kind":"arxiv","version":5},"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/2510.16892/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"}