{"id":189466,"date":"2013-06-11T00:00:00","date_gmt":"2013-06-11T17:55:37","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/learning-and-testing-submodular-functions\/"},"modified":"2016-08-02T06:12:34","modified_gmt":"2016-08-02T13:12:34","slug":"learning-and-testing-submodular-functions","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/learning-and-testing-submodular-functions\/","title":{"rendered":"Learning and testing submodular functions"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Submodular functions capture the law of diminishing returns and can be viewed as a generalization of convexity to functions over the Boolean cube. Such functions arise in different areas, such as combinatorial optimization, machine learning and economics. In this talk we will give a brief overview of recent structural results about concise  representations of submodular functions. Existence of small representations is  useful for applications in learning such functions from examples and testing whether a given function is submodular with a small number of queries.<\/p>\n<p>For the class submodular functions taking values in discrete integral range of size R we show a structural result, giving concise representation for this class by formulas. The representation can be described as a maximum over a collection of threshold functions, each expressed by an R-DNF formula. This leads to efficient PAC-style learning algorithms for this class, as well as testing algorithms with running time independent of the size of the domain.<\/p>\n<p>Joint work with Sofya Raskhodnikova (SODA&#8217;13) and work in progress with Eric Blais, Krzysztof Onak and Rocco Servedio<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Submodular functions capture the law of diminishing returns and can be viewed as a generalization of convexity to functions over the Boolean cube. Such functions arise in different areas, such as combinatorial optimization, machine learning and economics. In this talk we will give a brief overview of recent structural results about concise representations of submodular [&hellip;]<\/p>\n","protected":false},"featured_media":197670,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-189466","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/XDl86Gq0ucs","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/189466","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/189466\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197670"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=189466"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=189466"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=189466"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=189466"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=189466"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=189466"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=189466"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=189466"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=189466"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=189466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}