{"id":687636,"date":"2020-08-26T12:27:51","date_gmt":"2020-08-26T19:27:51","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=687636"},"modified":"2020-08-26T12:27:51","modified_gmt":"2020-08-26T19:27:51","slug":"error-correcting-tournaments","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/error-correcting-tournaments\/","title":{"rendered":"Error-Correcting Tournaments"},"content":{"rendered":"<p>We present a family of pairwise tournaments reducing\u00a0<span id=\"MathJax-Element-27-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-180\" class=\"math\"><span id=\"MathJax-Span-181\" class=\"mrow\"><span id=\"MathJax-Span-182\" class=\"mi\">k<\/span><\/span><\/span><\/span>-class classification to binary classification. These reductions are provably robust against a constant fraction of binary errors. The results improve on the PECOC construction \\cite{SECOC} with an exponential improvement in computation, from\u00a0<em><span id=\"MathJax-Element-28-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-183\" class=\"math\"><span id=\"MathJax-Span-184\" class=\"mrow\"><span id=\"MathJax-Span-185\" class=\"mi\">O<\/span><span id=\"MathJax-Span-186\" class=\"mo\">(<\/span><span id=\"MathJax-Span-187\" class=\"mi\">k<\/span><span id=\"MathJax-Span-188\" class=\"mo\">)<\/span><\/span><\/span><\/span><\/em>\u00a0to\u00a0<em><span id=\"MathJax-Element-29-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-189\" class=\"math\"><span id=\"MathJax-Span-190\" class=\"mrow\"><span id=\"MathJax-Span-191\" class=\"mi\">O<\/span><span id=\"MathJax-Span-192\" class=\"mo\">(<\/span><span id=\"MathJax-Span-193\" class=\"msubsup\"><span id=\"MathJax-Span-194\" class=\"mi\">log<\/span><span id=\"MathJax-Span-195\" class=\"mn\">2<\/span><\/span><span id=\"MathJax-Span-196\" class=\"mo\"><\/span><span id=\"MathJax-Span-197\" class=\"mi\">k<\/span><span id=\"MathJax-Span-198\" class=\"mo\">)<\/span><\/span><\/span><\/span><\/em>, and the removal of a square root in the regret dependence, matching the best possible computation and regret up to a constant.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a family of pairwise tournaments reducing\u00a0k-class classification to binary classification. These reductions are provably robust against a constant fraction of binary errors. The results improve on the PECOC construction \\cite{SECOC} with an exponential improvement in computation, from\u00a0O(k)\u00a0to\u00a0O(log2k), and the removal of a square root in the regret dependence, matching the best possible computation [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556],"msr-publication-type":[193724],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-687636","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2010-2","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":"https:\/\/arxiv.org\/abs\/0902.3176","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:\/\/arxiv.org\/pdf\/0902.3176.pdf","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Alina Beygelzimer","user_id":0,"rest_url":false},{"type":"user_nicename","value":"John Langford","user_id":32204,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=John Langford"},{"type":"text","value":"Pradeep Ravikumar","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199571],"msr_event":[],"msr_group":[144902,395930],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"miscellaneous","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/687636"}],"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\/687636\/revisions"}],"predecessor-version":[{"id":687642,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/687636\/revisions\/687642"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=687636"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=687636"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=687636"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=687636"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=687636"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=687636"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=687636"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=687636"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=687636"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=687636"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=687636"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=687636"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=687636"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=687636"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=687636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}