{"id":323291,"date":"2016-11-16T18:48:47","date_gmt":"2016-11-17T02:48:47","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=323291"},"modified":"2019-08-23T07:55:49","modified_gmt":"2019-08-23T14:55:49","slug":"measure-transformer-semantics-for-bayesian-machine-learning-2013","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/measure-transformer-semantics-for-bayesian-machine-learning-2013\/","title":{"rendered":"Measure Transformer Semantics for Bayesian Machine Learning"},"content":{"rendered":"

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define measure-transformer combinators inspired by theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that is processed by an existing inference engine for factor graphs, which are data structures that enable many efficient inference algorithms. This allows efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.<\/p>\n

\n

An abridged and extended version<\/a> of this paper appears in the proceedings of the 20th European Symposium on Programming (ESOP’11)<\/p>\n","protected":false},"excerpt":{"rendered":"

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561,13560],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-323291","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2013-9-9","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"Logical Methods in Computer Science","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"323294","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/11\/1308.0689.pdf","id":"323294","title":"Measure Transformer Semantics for Bayesian Machine Learning 1308-0689","label_id":"243109","label":0},{"type":"doi","viewUrl":"false","id":"false","title":"10.2168\/LMCS-9(3:11)2013","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Johannes Borgstr\u00f6m","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Andy Gordon","user_id":30825,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Andy Gordon"},{"type":"text","value":"Michael Greenberg","user_id":0,"rest_url":false},{"type":"text","value":"James Margetson","user_id":0,"rest_url":false},{"type":"text","value":"Jurgen Van Gael","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[169917],"publication":[],"video":[],"download":[],"msr_publication_type":"article","related_content":{"projects":[{"ID":169917,"post_title":"Infer.NET","post_name":"infernet","post_type":"msr-project","post_date":"2008-10-15 01:55:31","post_modified":"2023-04-06 09:14:43","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/infernet\/","post_excerpt":"Infer.NET is a .NET library for machine learning. It provides state-of-the-art algorithms for probabilistic inference from data. Various Bayesian models such as Bayes Point Machine classifiers, TrueSkill matchmaking, hidden Markov models, and Bayesian networks can be implemented using Infer.NET. Infer.NET is open source software under the MIT license. For more information about Infer.NET including documentation and examples please see the main Infer.NET page.","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/169917"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/323291"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/323291\/revisions"}],"predecessor-version":[{"id":525290,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/323291\/revisions\/525290"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=323291"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=323291"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=323291"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=323291"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=323291"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=323291"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=323291"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=323291"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=323291"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=323291"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=323291"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=323291"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=323291"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=323291"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=323291"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=323291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}