{"id":"https://openalex.org/W2141902405","doi":"https://doi.org/10.1145/1806689.1806786","title":"On the geometry of differential privacy","display_name":"On the geometry of differential privacy","publication_year":2010,"publication_date":"2010-06-05","ids":{"openalex":"https://openalex.org/W2141902405","doi":"https://doi.org/10.1145/1806689.1806786","mag":"2141902405"},"language":"en","primary_location":{"id":"doi:10.1145/1806689.1806786","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039915143","display_name":"Moritz Hardt","orcid":"https://orcid.org/0009-0000-7694-3038"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Moritz Hardt","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton University , Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University , Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080065269","display_name":"Kunal Talwar","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kunal Talwar","raw_affiliation_strings":["Microsoft Research, Silicon Valley, CA, USA","[Microsoft Research Silicon Valley, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Silicon Valley, CA, USA","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"[Microsoft Research Silicon Valley, CA, USA]","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039915143"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":35.8424,"has_fulltext":false,"cited_by_count":329,"citation_normalized_percentile":{"value":0.99797877,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"705","last_page":"714"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9764000177383423,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.9025954604148865},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8342969417572021},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6463714838027954},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6367279887199402},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6242454051971436},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.608649492263794},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5960988998413086},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.49088388681411743},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4842621684074402},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4806986451148987},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47242510318756104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46186476945877075},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.43021538853645325},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4188213348388672},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41168081760406494},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4113505482673645},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.33994895219802856},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3175959289073944},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.17172470688819885},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17137539386749268},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.16842150688171387},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09439346194267273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07832798361778259}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.9025954604148865},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8342969417572021},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6463714838027954},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6367279887199402},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6242454051971436},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.608649492263794},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5960988998413086},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.49088388681411743},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4842621684074402},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4806986451148987},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47242510318756104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46186476945877075},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.43021538853645325},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4188213348388672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41168081760406494},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4113505482673645},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.33994895219802856},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3175959289073944},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.17172470688819885},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17137539386749268},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.16842150688171387},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09439346194267273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07832798361778259},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1806689.1806786","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-second ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.163.3372","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.3372","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.psu.edu/~asmith/privacy598/papers/ht10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.312.1225","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.312.1225","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.3754v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.6427","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.6427","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.3754v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.359.9302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.359.9302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mrtz.org/papers/HT10geometry.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1483904091","https://openalex.org/W1487151840","https://openalex.org/W1549845494","https://openalex.org/W1557833142","https://openalex.org/W1564148078","https://openalex.org/W1809030594","https://openalex.org/W1873763122","https://openalex.org/W1993116423","https://openalex.org/W1999370902","https://openalex.org/W2010523825","https://openalex.org/W2022097286","https://openalex.org/W2023401026","https://openalex.org/W2036483997","https://openalex.org/W2041990574","https://openalex.org/W2050164782","https://openalex.org/W2063342497","https://openalex.org/W2087867172","https://openalex.org/W2094671291","https://openalex.org/W2097272254","https://openalex.org/W2100440346","https://openalex.org/W2101771965","https://openalex.org/W2109426455","https://openalex.org/W2110868467","https://openalex.org/W2112380340","https://openalex.org/W2115209166","https://openalex.org/W2120806354","https://openalex.org/W2123733729","https://openalex.org/W2124765629","https://openalex.org/W2154086287","https://openalex.org/W2169570643","https://openalex.org/W2296319761","https://openalex.org/W2913538792","https://openalex.org/W4256516376"],"related_works":["https://openalex.org/W4299565411","https://openalex.org/W1608366887","https://openalex.org/W2951386556","https://openalex.org/W4293468926","https://openalex.org/W4301080540","https://openalex.org/W3099415240","https://openalex.org/W2064868049","https://openalex.org/W2950343740","https://openalex.org/W2359798744","https://openalex.org/W2007366961"],"abstract_inverted_index":{"We":[0,42,60,80],"consider":[1],"the":[2,10,13,24,40,45,56,72,107,118],"noise":[3,46,73],"complexity":[4,47,74],"of":[5,58,88,109],"differentially":[6],"private":[7],"mechanisms":[8],"in":[9,31,39],"setting":[11],"where":[12],"user":[14],"asks":[15],"d":[16,77,84],"linear":[17,86,128],"queries":[18,87,129],"f:Rn":[19],"->":[20],"R":[21,32],"non-adaptively.":[22],"Here,":[23],"database":[25],"is":[26,37,48,92],"represented":[27],"by":[28,50],"a":[29,110],"vector":[30],"and":[33,68,94,134],"proximity":[34],"between":[35],"databases":[36],"measured":[38],"l1-metric.":[41],"show":[43,81],"that":[44,82],"determined":[49],"two":[51],"geometric":[52],"parameters":[53],"associated":[54],"with":[55],"set":[57],"queries.":[59],"use":[61],"this":[62],"connection":[63],"to":[64,96,102,126],"give":[65],"tight":[66],"upper":[67,133],"lower":[69,135],"bounds":[70],"on":[71],"for":[75,83],"any":[76],"\u2264":[78],"n.":[79],"random":[85],"sensitivity":[89],"1,":[90],"it":[91],"necessary":[93],"sufficient":[95],"add":[97],"l2-error":[98],"\u0398(min":[99],"d\u221ad/\u03b5,d\u221a(log":[100],"(n/d))/\u03b5)":[101],"achieve":[103],"\u03b5-differential":[104],"privacy.":[105],"Assuming":[106],"truth":[108],"deep":[111],"conjecture":[112],"from":[113],"convex":[114],"geometry,":[115],"known":[116],"as":[117],"Hyperplane":[119],"conjecture,":[120],"we":[121],"can":[122],"extend":[123],"our":[124],"results":[125],"arbitrary":[127],"giving":[130],"nearly":[131],"matching":[132],"bounds.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":33},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":21},{"year":2013,"cited_by_count":24},{"year":2012,"cited_by_count":28}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
