Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections.<\/p>\n","protected":false},"excerpt":{"rendered":"
Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. […]<\/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":"","msr-author-ordering":[{"type":"text","value":"Jack Raymond","user_id":0},{"type":"user_nicename","value":"Andre Manoel","user_id":"40504"},{"type":"text","value":"Manfred Opper","user_id":0}],"msr_publishername":"Oxford University Press","msr_publisher_other":"","msr_booktitle":"Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"978-0198743736","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"263\u2013292","msr_page_range_start":"263","msr_page_range_end":"292","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_mag_id":"3037286129","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_release_tracker_id":"","msr_highlight_type":"","msr_date_display_format":"","msr_main_download_label":"","msr_external_link_label":"","msr_doi_label":"","msr_published_date":"2016-02-17","msr_startdate":"","msr_presentation_date":"","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_year":2016,"msr_month":2,"msr_day":17,"msr_microsoftintellectualproperty":false,"msr_pub_id":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":false,"title":"https:\/\/arxiv.org\/abs\/1409.6179","label_id":243109,"label":0}],"msr_related_uploader":[],"msr_original_fields_of_study":["Computer science","Inference","Expectation propagation","Connection (mathematics)","Calculus","Iterative approximation"],"msr_s2_paper_id":"","msr_s2_pdf_url":"","msr_citation_count_updated":"","msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13556],"msr-publication-type":[193721],"msr-publisher":[],"msr-publication-cta":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[258214,246691,258211,258208,248668,258217],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-760783","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us","msr-field-of-study-calculus","msr-field-of-study-computer-science","msr-field-of-study-connection-mathematics","msr-field-of-study-expectation-propagation","msr-field-of-study-inference","msr-field-of-study-iterative-approximation"],"msr_publishername":"Oxford University Press","msr_edition":"","msr_affiliation":"","msr_published_date":"2016-02-17","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue","msr_pages_string":"263\u2013292","msr_chapter":"","msr_isbn":"978-0198743736","msr_journal":"","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":0,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/1409.6179","label_id":"243109","label":0}],"msr_related_uploader":[],"msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Jack Raymond","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Andre Manoel","user_id":40504,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Andre Manoel"},{"type":"text","value":"Manfred Opper","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inbook","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/760783","targetHints":{"allow":["GET"]}}],"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\/760783\/revisions"}],"predecessor-version":[{"id":760786,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/760783\/revisions\/760786"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=760783"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=760783"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=760783"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=760783"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=760783"},{"taxonomy":"msr-publication-cta","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-cta?post=760783"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=760783"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=760783"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=760783"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=760783"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=760783"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=760783"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=760783"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=760783"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}