{"id":"https://openalex.org/W2043969662","doi":"https://doi.org/10.1145/2488608.2488650","title":"Beyond worst-case analysis in private singular vector computation","display_name":"Beyond worst-case analysis in private singular vector computation","publication_year":2013,"publication_date":"2013-05-28","ids":{"openalex":"https://openalex.org/W2043969662","doi":"https://doi.org/10.1145/2488608.2488650","mag":"2043969662"},"language":"en","primary_location":{"id":"doi:10.1145/2488608.2488650","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2488608.2488650","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-fifth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Moritz Hardt","raw_affiliation_strings":["IBM Research Almaden, San Jose, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research Almaden, San Jose, USA","institution_ids":["https://openalex.org/I4210085935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057693522","display_name":"Aaron Roth","orcid":"https://orcid.org/0000-0002-0586-0515"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]},{"id":"https://openalex.org/I922845939","display_name":"Philadelphia University","ror":"https://ror.org/03zzmyz63","country_code":"US","type":"education","lineage":["https://openalex.org/I922845939"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron Roth","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, USA","institution_ids":["https://openalex.org/I922845939","https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"331","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9986000061035156,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.7236117124557495},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6976636052131653},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6769755482673645},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6182315945625305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5375129580497742},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.49460312724113464},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.47314465045928955},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45532962679862976},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.4502888023853302},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4423532485961914},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.43749749660491943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39607226848602295},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3442884087562561},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33885395526885986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3327457904815674},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.23688635230064392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.190879225730896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14059770107269287},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10729151964187622}],"concepts":[{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.7236117124557495},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6976636052131653},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6769755482673645},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6182315945625305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5375129580497742},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.49460312724113464},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.47314465045928955},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45532962679862976},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4502888023853302},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4423532485961914},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.43749749660491943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39607226848602295},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3442884087562561},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33885395526885986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3327457904815674},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23688635230064392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.190879225730896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14059770107269287},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10729151964187622},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2488608.2488650","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2488608.2488650","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-fifth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1586209290","https://openalex.org/W1982147025","https://openalex.org/W1985310469","https://openalex.org/W1993116423","https://openalex.org/W2010523825","https://openalex.org/W2028584480","https://openalex.org/W2110868467","https://openalex.org/W2134332047","https://openalex.org/W2135930857","https://openalex.org/W2160955670","https://openalex.org/W2167372639","https://openalex.org/W2401095126","https://openalex.org/W2611328865","https://openalex.org/W2963723438","https://openalex.org/W4239784985","https://openalex.org/W6628979892"],"related_works":["https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W3017414697","https://openalex.org/W3206304544","https://openalex.org/W3174042135","https://openalex.org/W2006601391","https://openalex.org/W2962791795","https://openalex.org/W2409839127"],"abstract_inverted_index":{"We":[0,31,67],"consider":[1],"differentially":[2,18],"private":[3,19],"approximate":[4],"singular":[5,29],"vector":[6],"computation.":[7],"Known":[8],"worst-case":[9,117],"lower":[10,72],"bounds":[11,92],"show":[12],"that":[13,52,75],"the":[14,25,28,39,47,50,61,85,99,125],"error":[15],"of":[16,27,49,84,98,107],"any":[17],"algorithm":[20,111],"must":[21],"scale":[22],"polynomially":[23],"with":[24],"dimension":[26,40,62],"vector.":[30],"are":[32],"able":[33],"to":[34,56,114,120],"replace":[35],"this":[36],"dependence":[37],"on":[38],"by":[41,93],"a":[42,70,95],"natural":[43],"parameter":[44],"known":[45],"as":[46],"coherence":[48,86],"matrix":[51],"is":[53,78],"often":[54],"observed":[55],"be":[57,106],"significantly":[58],"smaller":[59],"than":[60],"both":[63],"theoretically":[64],"and":[65,119],"empirically.":[66],"also":[68,112],"prove":[69],"matching":[71],"bound":[73],"showing":[74],"our":[76,91],"guarantee":[77],"nearly":[79],"optimal":[80],"for":[81],"every":[82],"setting":[83],"parameter.":[87],"Notably,":[88],"we":[89],"achieve":[90],"giving":[94],"robust":[96],"analysis":[97],"well-known":[100],"power":[101],"iteration":[102],"algorithm,":[103],"which":[104],"may":[105],"independent":[108],"interest.":[109],"Our":[110],"leads":[113],"improvements":[115],"in":[116,124],"settings":[118],"better":[121],"low-rank":[122],"approximations":[123],"spectral":[126],"norm.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":10}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
