Recently Kutin and Niyogi investigated several notions of algorithmic stability–a property of a learning map conceptually similar to continuity–showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free CV-stability is necessary and sufficient for having finite VC-dimension. This paper concerns a phase transition in the training stability of ERM, conjectured by the same authors. Kutin and Niyogi proved that ERM on finite hypothesis spaces containing a unique risk minimizer has training stability that scales exponentially with sample size, and conjectured that the existence of multiple risk minimizers prevents even super-quadratic convergence. We prove this result for the strictly weaker notion of CV-stability, positively resolving the conjecture.<\/p>\n","protected":false},"excerpt":{"rendered":"
Recently Kutin and Niyogi investigated several notions of algorithmic stability–a property of a learning map conceptually similar to continuity–showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free CV-stability is necessary and sufficient for having finite VC-dimension. This paper concerns a phase transition in the training stability of ERM, conjectured by the […]<\/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":"user_nicename","value":"berubins","user_id":"31213"}],"msr_publishername":"IEEE","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"IEEE Transactions on Information Theory","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"IEEE Transactions on Information Theory","msr_number":"7","msr_organization":"","msr_pages_string":"4160-4163","msr_page_range_start":"4160","msr_page_range_end":"4163","msr_series":"","msr_volume":"58","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2012-07-01","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/arxiv.org\/abs\/1002.2044","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2012,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-162495","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"IEEE","msr_edition":"IEEE Transactions on Information Theory","msr_affiliation":"","msr_published_date":"2012-07-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"4160-4163","msr_chapter":"","msr_isbn":"","msr_journal":"IEEE Transactions on Information Theory","msr_volume":"58","msr_number":"7","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":"http:\/\/arxiv.org\/abs\/1002.2044","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"http:\/\/arxiv.org\/abs\/1002.2044","viewUrl":false,"id":false,"label_id":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":[{"id":0,"url":"http:\/\/arxiv.org\/abs\/1002.2044"}],"msr-author-ordering":[{"type":"user_nicename","value":"berubins","user_id":31213,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=berubins"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"article","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/162495","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\/162495\/revisions"}],"predecessor-version":[{"id":516020,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/162495\/revisions\/516020"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=162495"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=162495"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=162495"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=162495"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=162495"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=162495"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=162495"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=162495"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=162495"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=162495"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=162495"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=162495"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=162495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}