Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R’s formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.<\/p>\n","protected":false},"excerpt":{"rendered":"
Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, […]<\/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":[13556,13560],"msr-publication-type":[193716],"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-606135","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2016-1-1","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","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":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/dl.acm.org\/citation.cfm?doid=2837614.2837653","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":"Long Ouyang","user_id":0,"rest_url":false},{"type":"text","value":"Claudio Russo","user_id":0,"rest_url":false},{"type":"text","value":"Adam \u015acibior","user_id":0,"rest_url":false},{"type":"text","value":"Marcin Szymczak","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199561],"msr_event":[],"msr_group":[],"msr_project":[511097,387230],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":511097,"post_title":"Calc Intelligence","post_name":"calc-intelligence","post_type":"msr-project","post_date":"2020-02-17 06:40:29","post_modified":"2023-11-27 06:33:39","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/calc-intelligence\/","post_excerpt":"By Calc Intelligence, we mean the research goal of bringing intelligence to end-user programming, and in particular to spreadsheets.","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/511097"}]}},{"ID":387230,"post_title":"Tabular","post_name":"tabular","post_type":"msr-project","post_date":"2017-05-29 23:46:26","post_modified":"2017-05-30 00:33:16","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/tabular\/","post_excerpt":"Tabular is a Excel add-in that brings the power of model based machine learning to data enthusiasts. 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