{"id":"https://openalex.org/W7204961592","doi":"https://doi.org/10.48550/arxiv.2608.31138","title":"Scale Analysis and Shape Selection for the Generalized Gaussian Mechanism under Approximate Differential Privacy","display_name":"Scale Analysis and Shape Selection for the Generalized Gaussian Mechanism under Approximate Differential Privacy","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204961592","doi":"https://doi.org/10.48550/arxiv.2608.31138"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.31138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31138","pdf_url":"https://arxiv.org/pdf/2608.31138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.31138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123347262","display_name":"Xiang Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048159918","display_name":"Mohamedou Ould Haye","orcid":"https://orcid.org/0000-0002-6274-3374","observed_orcids":["https://orcid.org/0000-0002-6274-3374"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haye, Mohamedou Ould","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139234431","display_name":"Yiqiang Q. Zhao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Yiqiang Q.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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/T11614","display_name":"Cloud Data Security Solutions","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/approximate-differential-privacy","display_name":"approximate differential privacy","score":0.9440000057220459},{"id":"https://openalex.org/keywords/epsilon-delta-differential-privacy","display_name":"(\u03b5, \u03b4)-differential privacy","score":0.8970000147819519},{"id":"https://openalex.org/keywords/scale-parameter-estimation","display_name":"scale parameter estimation","score":0.5509999990463257},{"id":"https://openalex.org/keywords/shape-parameter-selection","display_name":"shape parameter selection","score":0.9419999718666077},{"id":"https://openalex.org/keywords/generalized-gaussian-noise","display_name":"generalized Gaussian noise","score":0.7590000033378601},{"id":"https://openalex.org/keywords/privacy-utility-trade-off","display_name":"privacy-utility trade-off","score":0.7110000252723694},{"id":"https://openalex.org/keywords/sensitivity-vectors","display_name":"sensitivity vectors","score":0.5960000157356262}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.8497999906539917},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6195999979972839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6057999730110168},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.49900001287460327},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4959000051021576},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.492900013923645},{"id":"https://openalex.org/C199435849","wikidata":"https://www.wikidata.org/wiki/Q3179293","display_name":"Shape parameter","level":2,"score":0.47360000014305115},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4675999879837036},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4505999982357025},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4433000087738037},{"id":"https://openalex.org/C91716921","wikidata":"https://www.wikidata.org/wiki/Q1289366","display_name":"Scale parameter","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4212999939918518},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40689998865127563},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.36559998989105225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36239999532699585},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.31940001249313354},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C183057437","wikidata":"https://www.wikidata.org/wiki/Q671617","display_name":"Laplace distribution","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.28209999203681946},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.31138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31138","pdf_url":"https://arxiv.org/pdf/2608.31138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.31138","doi":"https://doi.org/10.48550/arxiv.2608.31138","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.31138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31138","pdf_url":"https://arxiv.org/pdf/2608.31138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204961592.pdf","grobid_xml":"https://content.openalex.org/works/W7204961592.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2284973007","https://openalex.org/W2963126806","https://openalex.org/W3165236375","https://openalex.org/W4205228770","https://openalex.org/W6966529677"],"related_works":["https://openalex.org/W2284973007","https://openalex.org/W2990741518","https://openalex.org/W4415111878","https://openalex.org/W7164004597","https://openalex.org/W7162691626","https://openalex.org/W3199765715","https://openalex.org/W3165236375","https://openalex.org/W4291248000","https://openalex.org/W2796603110","https://openalex.org/W4376639623"],"abstract_inverted_index":{"Differential":[0],"privacy":[1,96,126,184,225],"provides":[2],"a":[3,24,73,108,117,132,208],"rigorous":[4],"framework":[5],"for":[6,90],"protecting":[7],"private":[8],"information,":[9],"typically":[10],"achieved":[11],"by":[12,32,107,196,203],"adding":[13],"random":[14],"noise":[15,29],"to":[16,205],"query":[17],"results.":[18],"The":[19],"generalized":[20,65],"Gaussian":[21,42,66],"family":[22],"is":[23],"flexible":[25],"class":[26],"of":[27,63,86,110,121,167,173,200,210,224],"additive":[28],"distributions":[30,43],"indexed":[31],"the":[33,39,54,59,64,83,87,92,99,125,137,142,165,168,174,198,221],"shape":[34,60,149,170,191,232],"parameter":[35,61,89],"$p$":[36],"and":[37,41,48,58,78,177],"includes":[38],"Laplace":[40],"as":[44,141],"special":[45],"cases":[46,214],"$p=1$":[47],"$p=2$,":[49],"respectively.":[50],"This":[51],"paper":[52],"studies":[53],"privacy-feasible":[55],"scale":[56,88],"estimation":[57],"selection":[62],"mechanism":[67,93],"(GGM)":[68],"under":[69,131,171,182],"$(\\varepsilon,\u03b4)$-differential":[70],"privacy.":[71],"For":[72,112],"given":[74],"sensitivity":[75,175],"vector":[76,176],"$\u0394$":[77],"$p\\in[1,\\infty]$,":[79],"let":[80],"$b(p)$":[81,102,122],"denote":[82],"smallest":[84],"value":[85],"which":[91],"satisfies":[94],"this":[95],"requirement.":[97],"In":[98],"one-dimensional":[100],"case,":[101],"can":[103,157,193,234],"be":[104,158],"implicitly":[105],"characterized":[106],"system":[109],"equations.":[111],"vector-valued":[113],"queries,":[114],"we":[115],"construct":[116],"computable":[118],"upper":[119],"approximation":[120,154],"that":[123,156,189,231],"preserves":[124],"guarantee.":[127],"Shapes":[128],"are":[129],"compared":[130],"scale-homogeneous":[133],"utility":[134,195],"criterion,":[135],"with":[136,152,212],"$m$-th":[138],"absolute":[139],"moment":[140],"main":[143],"example.":[144],"We":[145,162],"develop":[146],"an":[147,153],"interval-wise":[148],"search":[150],"algorithm":[151],"guarantee":[155],"made":[159],"arbitrarily":[160],"precise.":[161],"also":[163],"establish":[164],"invariance":[166],"optimal":[169],"rescaling":[172],"characterize":[178],"its":[179],"limiting":[180],"behaviour":[181],"high":[183],"limits.":[185],"Computational":[186],"experiments":[187,228],"show":[188,230],"optimizing":[190],"parameters":[192],"improve":[194,235],"reducing":[197],"variance":[199],"each":[201],"coordinate":[202],"5%":[204],"20%":[206],"across":[207],"variety":[209],"cases,":[211],"some":[213],"showing":[215],"even":[216],"greater":[217],"reductions,":[218],"while":[219],"maintaining":[220],"same":[222],"level":[223],"protection.":[226],"Task-specific":[227],"further":[229],"optimization":[233],"task-level":[236],"utility,":[237],"reduce":[238],"attacker":[239],"success,":[240],"or":[241],"achieve":[242],"both.":[243]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
