{"id":"https://openalex.org/W7214217205","doi":"https://doi.org/10.48550/arxiv.2609.28297","title":"Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions","display_name":"Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214217205","doi":"https://doi.org/10.48550/arxiv.2609.28297"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28297","pdf_url":"https://arxiv.org/pdf/2609.28297","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/2609.28297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093063025","display_name":"Leonhard Grosse","orcid":"https://orcid.org/0000-0002-7192-8418","observed_orcids":["https://orcid.org/0000-0002-7192-8418"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grosse, Leonhard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008260742","display_name":"Sara Saeidian","orcid":"https://orcid.org/0000-0001-6908-559X","observed_orcids":["https://orcid.org/0000-0001-6908-559X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saeidian, Sara","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079492269","display_name":"Tobias J. Oechtering","orcid":"https://orcid.org/0000-0002-0036-9049","observed_orcids":["https://orcid.org/0000-0002-0036-9049"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oechtering, Tobias J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041348422","display_name":"Mikael Skoglund","orcid":"https://orcid.org/0000-0002-7926-5081","observed_orcids":["https://orcid.org/0000-0002-7926-5081"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Skoglund, Mikael","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":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/T10764","display_name":"Privacy-Preserving Technologies in Data","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/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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","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/local-differential-privacy","display_name":"local differential privacy","score":0.7549999952316284},{"id":"https://openalex.org/keywords/contraction-analysis","display_name":"contraction analysis","score":0.8659999966621399},{"id":"https://openalex.org/keywords/disclosure-control","display_name":"disclosure control","score":0.9229999780654907},{"id":"https://openalex.org/keywords/data-processing-inequality","display_name":"data processing inequality","score":0.6140000224113464},{"id":"https://openalex.org/keywords/f-divergence","display_name":"f-divergence","score":0.9750000238418579},{"id":"https://openalex.org/keywords/mean-estimation","display_name":"mean estimation","score":0.8799999952316284},{"id":"https://openalex.org/keywords/privacy-leakage","display_name":"privacy leakage","score":0.5040000081062317},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"sample complexity","score":0.5070000290870667}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6801999807357788},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.6639999747276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6532999873161316},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6114000082015991},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.49729999899864197},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4797999858856201},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4472000002861023},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4108999967575073},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.37950000166893005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3582000136375427},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3407999873161316},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3156999945640564},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.302700012922287},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.2953999936580658},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C58948655","wikidata":"https://www.wikidata.org/wiki/Q7604392","display_name":"Statistical distance","level":3,"score":0.2833000123500824},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26980000734329224},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2547999918460846},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.2547999918460846},{"id":"https://openalex.org/C2779201187","wikidata":"https://www.wikidata.org/wiki/Q2775060","display_name":"Information leakage","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28297","pdf_url":"https://arxiv.org/pdf/2609.28297","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.2609.28297","doi":"https://doi.org/10.48550/arxiv.2609.28297","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28297","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28297","pdf_url":"https://arxiv.org/pdf/2609.28297","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/W7214217205.pdf","grobid_xml":"https://content.openalex.org/works/W7214217205.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2273160922","https://openalex.org/W2289921170","https://openalex.org/W4287550283","https://openalex.org/W4407571378","https://openalex.org/W4414812185","https://openalex.org/W4417531119","https://openalex.org/W6948027376","https://openalex.org/W7110162628","https://openalex.org/W7124279250","https://openalex.org/W7124454805","https://openalex.org/W7163443385"],"related_works":["https://openalex.org/W7124270496","https://openalex.org/W3198855841","https://openalex.org/W3127564821","https://openalex.org/W4320509002","https://openalex.org/W4396782890","https://openalex.org/W7125690900","https://openalex.org/W2784761289","https://openalex.org/W4386065969","https://openalex.org/W7048792564","https://openalex.org/W4289655248"],"abstract_inverted_index":{"We":[0,66,82,130],"investigate":[1],"$c$-interior":[2,26,46,92,143],"pointwise":[3],"maximal":[4,24],"leakage":[5,181],"(PML)":[6],"as":[7,48],"a":[8,53,120,168,198],"tool":[9],"for":[10,146],"contraction":[11,61,77],"analyses":[12,62,204],"and":[13,74,137,150,185],"disclosure":[14,157,203],"control.":[15],"Based":[16],"on":[17,52,70,89],"the":[18,71,76,80,96,100,107,113,132,179,202,208,215],"strong":[19,85],"adversarial":[20,189],"threat":[21],"models":[22],"from":[23,41],"leakage,":[25],"PML":[27,47,93,144,160],"generalizes":[28],"local":[29],"differential":[30],"privacy":[31,180,209],"(LDP)":[32],"to":[33,99,104,118,134,163,177,193],"data-generating":[34],"distributions":[35,98],"with":[36,159,191],"densities":[37],"uniformly":[38],"bounded":[39],"away":[40],"zero":[42],"by":[43],"$c>0$.":[44],"Viewing":[45],"an":[49],"algebraic":[50],"constraint":[51],"kernel":[54],"yields":[55],"more":[56,169],"flexible":[57],"(and":[58],"often":[59],"tighter)":[60],"than":[63],"standard":[64],"LDP.":[65],"provide":[67,138],"tight":[68],"bounds":[69],"Dobrushin":[72],"coefficient,":[73],"bound":[75,217],"coefficient":[78],"of":[79,115,123,182,233],"Hockeystick-divergence.":[81],"further":[83],"derive":[84],"data":[86],"processing":[87],"inequalities":[88],"$f$-divergences":[90],"under":[91,142],"constraints":[94,145],"when":[95],"input":[97],"divergence":[101],"are":[102],"restricted":[103],"be":[105,224],"in":[106,167,201,231],"$c$-interior.":[108],"These":[109],"results":[110,133,154],"extend":[111],"beyond":[112],"regime":[114],"pure":[116],"LDP":[117],"cover":[119],"larger":[121],"class":[122],"kernels,":[124],"including,":[125],"e.g.,":[126],"arbitrary":[127,194],"stochastic":[128],"matrices.":[129],"apply":[131],"minimax":[135],"theory":[136],"asymptotically":[139],"optimal":[140],"strategies":[141],"binary":[147],"hypothesis":[148],"testing":[149],"mean":[151],"estimation.":[152],"The":[153],"show":[155],"that":[156,206],"control":[158],"allows":[161,175],"analysts":[162],"reason":[164],"about":[165],"systems":[166],"differentiated":[170],"manner:":[171],"For":[172],"example,":[173],"it":[174],"us":[176],"quantify":[178],"deterministic":[183],"systems,":[184],"can":[186,223],"give":[187],"precise":[188],"guarantees":[190],"respect":[192],"distributional":[195],"assumptions.":[196],"Interestingly,":[197],"recurring":[199],"theme":[200],"is":[205,211,219],"if":[207],"problem":[210],"relatively":[212],"regular":[213],"(if":[214],"density":[216],"$c$":[218],"large),":[220],"private":[221],"inference":[222],"possible":[225],"without":[226],"incurring":[227],"any":[228],"additional":[229],"cost":[230],"terms":[232],"sample":[234],"complexity.":[235]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}