{"id":639414,"date":"2020-02-26T12:19:06","date_gmt":"2020-02-26T20:19:06","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=639414"},"modified":"2022-03-29T13:44:54","modified_gmt":"2022-03-29T20:44:54","slug":"differentially-private-set-union","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/differentially-private-set-union\/","title":{"rendered":"Differentially Private Set Union"},"content":{"rendered":"

We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe\u00a0U<\/span><\/span><\/span><\/span>\u00a0of items, possibly of infinite size, and a database\u00a0D<\/span><\/span><\/span><\/span>\u00a0of users. Each user\u00a0i<\/span><\/span><\/span><\/span>\u00a0contributes a subset\u00a0W<\/span><\/span>\u2286<\/span>U<\/span><\/span><\/span><\/span>\u00a0of items. We want an (\u03f5<\/span><\/span><\/span><\/span>,\u03b4<\/span><\/span><\/span><\/span>)-differentially private algorithm which outputs a subset\u00a0S of the union of all sets <\/span>W<\/span><\/span><\/span><\/span><\/span>\u00a0such that the size of\u00a0S<\/span><\/span><\/span><\/span>\u00a0is as large as possible. The problem arises in countless real world applications; it is particularly ubiquitous in natural language processing (NLP) applications as vocabulary extraction. For example, discovering words, sentences,\u00a0n<\/span><\/span><\/span><\/span>-grams etc., from private text data belonging to users is an instance of the set union problem.<\/p>\n

Known algorithms for this problem proceed by collecting a subset of items from each user, taking the union of such subsets, and disclosing the items whose noisy counts fall above a certain threshold. Crucially, in the above process, the contribution of each individual user is always independent of the items held by other users, resulting in a wasteful aggregation process, where some item counts happen to be way above the threshold. We deviate from the above paradigm by allowing users to contribute their items in a dependent fashion<\/span><\/span><\/span><\/span><\/span><\/span>, guided by a\u00a0policy<\/span><\/span><\/span><\/span><\/span><\/span>. In this new setting ensuring privacy is significantly delicate. We prove that any policy which has certain\u00a0contractive<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0properties would result in a differentially private algorithm. We design two new algorithms, one using Laplace noise and other Gaussian noise, as specific instances of policies satisfying the contractive properties. Our experiments show that the new algorithms significantly outperform previously known mechanisms for the problem.<\/p>\n","protected":false},"excerpt":{"rendered":"

We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe\u00a0U\u00a0of items, possibly of infinite size, and a database\u00a0D\u00a0of users. Each user\u00a0i\u00a0contributes a subset\u00a0W\u2286U\u00a0of items. We want an (\u03f5,\u03b4)-differentially private algorithm which outputs a subset\u00a0S of the union of all sets W\u00a0such that […]<\/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":[13561,13546,13558],"msr-publication-type":[193716],"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-639414","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2020-7-1","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":"Contributed talk at TPDP 2020. Also appeared in the Journal of Privacy and Confidentiality (JPC).","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:\/\/journalprivacyconfidentiality.org\/index.php\/jpc\/article\/view\/780","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[{"id":639420,"url":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2020\/02\/Differentially-Private-Set-Union.pdf"}],"msr-author-ordering":[{"type":"user_nicename","value":"Sivakanth Gopi","user_id":37830,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Sivakanth Gopi"},{"type":"text","value":"Pankaj Gulhane","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Janardhan (Jana) Kulkarni","user_id":32147,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Janardhan (Jana) Kulkarni"},{"type":"text","value":"Judy Hanwen Shen","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Milad Shokouhi","user_id":32921,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Milad Shokouhi"},{"type":"user_nicename","value":"Sergey Yekhanin","user_id":34990,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Sergey Yekhanin"}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[644373,761911],"msr_project":[556311],"publication":[],"video":[],"download":[669690],"msr_publication_type":"inproceedings","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/639414"}],"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":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/639414\/revisions"}],"predecessor-version":[{"id":639453,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/639414\/revisions\/639453"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=639414"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=639414"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=639414"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=639414"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=639414"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=639414"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=639414"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=639414"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=639414"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=639414"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=639414"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=639414"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=639414"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=639414"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=639414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}