{"id":555654,"date":"2018-11-01T07:01:41","date_gmt":"2018-11-01T14:01:41","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=555654"},"modified":"2018-12-05T07:05:51","modified_gmt":"2018-12-05T15:05:51","slug":"private-algorithms-can-always-be-extended","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/private-algorithms-can-always-be-extended\/","title":{"rendered":"Private Algorithms Can Always Be Extended"},"content":{"rendered":"

We consider the following fundamental question on \u03b5<\/span><\/span><\/span><\/span><\/span><\/span>-differential privacy. Consider an arbitrary \u03b5<\/span><\/span><\/span><\/span><\/span><\/span>-differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an \u03b5<\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span>-differentially private algorithm on the whole input space for some \u03b5<\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span> comparable with \u03b5<\/span><\/span><\/span><\/span><\/span><\/span>? In this note we answer affirmatively this question for \u03b5<\/span><\/span><\/span>\u2032<\/span><\/span>=<\/span>2<\/span>\u03b5<\/span><\/span><\/span><\/span><\/span><\/span>. Our result applies to every input metric space and space of possible outputs. This result originally appeared in a recent paper by the authors [BCSZ18]. We present a self-contained version in this note, in the hopes that it will be broadly useful.<\/p>\n","protected":false},"excerpt":{"rendered":"

We consider the following fundamental question on \u03b5-differential privacy. Consider an arbitrary \u03b5-differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an \u03b5\u2032-differentially private algorithm on the whole input space for some \u03b5\u2032 comparable with \u03b5? In this note we answer affirmatively this question for \u03b5\u2032=2\u03b5. […]<\/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":[13561],"msr-publication-type":[193726],"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-555654","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2018-11-1","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:\/\/arxiv.org\/abs\/1810.12518","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"Christian 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