{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T20:22:43Z","timestamp":1789935763013,"version":"4.0.1"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,9,9]],"date-time":"2013-09-09T00:00:00Z","timestamp":1378684800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The Bayesian approach to machine learning amounts to computing posterior\ndistributions of random variables from a probabilistic model of how the\nvariables are related (that is, a prior distribution) and a set of observations\nof variables. There is a trend in machine learning towards expressing Bayesian\nmodels as probabilistic programs. As a foundation for this kind of programming,\nwe propose a core functional calculus with primitives for sampling prior\ndistributions and observing variables. We define measure-transformer\ncombinators inspired by theorems in measure theory, and use these to give a\nrigorous semantics to our core calculus. The original features of our semantics\ninclude its support for discrete, continuous, and hybrid measures, and, in\nparticular, for observations of zero-probability events. We compile our core\nlanguage to a small imperative language that is processed by an existing\ninference engine for factor graphs, which are data structures that enable many\nefficient inference algorithms. This allows efficient approximate inference of\nposterior marginal distributions, treating thousands of observations per second\nfor large instances of realistic models.<\/jats:p>","DOI":"10.2168\/lmcs-9(3:11)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:44:29Z","timestamp":1385732669000},"source":"Crossref","is-referenced-by-count":11,"title":["Measure Transformer Semantics for Bayesian Machine Learning"],"prefix":"10.46298","volume":"Volume 9, Issue 3","author":[{"given":"Johannes","family":"Borgstr\u00f6m","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew D","family":"Gordon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0014-7670","authenticated-orcid":false,"given":"Michael","family":"Greenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Margetson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jurgen","family":"Van Gael","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2013,9,9]]},"reference":[{"key":"908:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/815\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/815\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:56:37Z","timestamp":1681242997000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,9]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(3:11)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1308.0689","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1308.0689","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"doi","id":"10.1101\/161125","asserted-by":"subject"},{"id-type":"doi","id":"10.3389\/fevo.2019.00402","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,9]]},"article-number":"815"}}