{"id":"https://openalex.org/W7222111998","doi":"https://doi.org/10.48550/arxiv.2610.19573","title":"On Inherent Privacy of Posterior Sampling: A Unified R\u00e9nyi-Divergence Framework","display_name":"On Inherent Privacy of Posterior Sampling: A Unified R\u00e9nyi-Divergence Framework","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7222111998","doi":"https://doi.org/10.48550/arxiv.2610.19573"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.19573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19573","pdf_url":"https://arxiv.org/pdf/2610.19573","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":"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/2610.19573","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158805196","display_name":"Ruyu Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhou, Ruyu","raw_affiliation_strings":["Department of Computer Science and Statistics University of Rhode Island"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Statistics University of Rhode Island","institution_ids":["https://openalex.org/I17626003"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158847572","display_name":"Fang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Fang","raw_affiliation_strings":["Department of ACMS University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ACMS University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.0,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-privacy","display_name":"differential privacy","score":0.9879999756813049},{"id":"https://openalex.org/keywords/posterior-sampling","display_name":"posterior sampling","score":0.8059999942779541},{"id":"https://openalex.org/keywords/renyi-divergence","display_name":"R\u00e9nyi divergence","score":0.9390000104904175},{"id":"https://openalex.org/keywords/bayesian-posterior-distribution","display_name":"Bayesian posterior distribution","score":0.7300000190734863},{"id":"https://openalex.org/keywords/exponential-moments","display_name":"exponential moments","score":0.671999990940094},{"id":"https://openalex.org/keywords/log-likelihood-ratio","display_name":"log-likelihood ratio","score":0.9150000214576721},{"id":"https://openalex.org/keywords/sub-gaussian-tails","display_name":"sub-Gaussian tails","score":0.7919999957084656},{"id":"https://openalex.org/keywords/generalized-linear-models","display_name":"generalized linear models","score":0.9639999866485596},{"id":"https://openalex.org/keywords/linear-regression","display_name":"linear regression","score":0.8159999847412109},{"id":"https://openalex.org/keywords/gaussian-prior","display_name":"Gaussian prior","score":0.5899999737739563}],"concepts":[{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.6150000095367432},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.5863000154495239},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5108000040054321},{"id":"https://openalex.org/C26004113","wikidata":"https://www.wikidata.org/wiki/Q3711784","display_name":"Conjugate prior","level":4,"score":0.5074999928474426},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.47350001335144043},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.47269999980926514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4699999988079071},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3862999975681305},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.35260000824928284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3386000096797943},{"id":"https://openalex.org/C73602740","wikidata":"https://www.wikidata.org/wiki/Q7795822","display_name":"Thompson sampling","level":3,"score":0.33320000767707825},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.3312000036239624},{"id":"https://openalex.org/C37903108","wikidata":"https://www.wikidata.org/wiki/Q4874474","display_name":"Bayesian linear regression","level":4,"score":0.31940001249313354},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.30410000681877136},{"id":"https://openalex.org/C123201435","wikidata":"https://www.wikidata.org/wiki/Q456632","display_name":"Information privacy","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2937000095844269},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C41587187","wikidata":"https://www.wikidata.org/wiki/Q1501882","display_name":"Generalized linear model","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.19573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19573","pdf_url":"https://arxiv.org/pdf/2610.19573","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.19573","doi":"https://doi.org/10.48550/arxiv.2610.19573","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.19573","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:2610.19573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19573","pdf_url":"https://arxiv.org/pdf/2610.19573","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222111998.pdf","grobid_xml":"https://content.openalex.org/works/W7222111998.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2054922243","https://openalex.org/W4302011600","https://openalex.org/W4392781355"],"related_works":["https://openalex.org/W2963828152","https://openalex.org/W2260885507","https://openalex.org/W4223972154","https://openalex.org/W3201845924","https://openalex.org/W7164995266","https://openalex.org/W7214221806","https://openalex.org/W2580411275","https://openalex.org/W7133243738","https://openalex.org/W4392781355","https://openalex.org/W2608609295"],"abstract_inverted_index":{"Differential":[0],"Privacy":[1],"(DP)":[2],"provides":[3],"a":[4,41,55],"rigorous":[5],"framework":[6,45,96],"for":[7,166,187],"quantifying":[8],"privacy":[9,63,175],"guarantees.":[10],"While":[11],"most":[12],"methods":[13],"achieve":[14],"DP":[15,32,50,83,141,154,164,191],"by":[16,66,71],"injecting":[17],"calibrated":[18],"random":[19],"noise,":[20],"the":[21,48,62,76,95,114,128,152,162,182,189],"intrinsic":[22],"randomness":[23],"of":[24,52,75,156,184,193],"certain":[25],"procedures":[26],"such":[27],"as":[28,168],"sampling":[29,53],"can":[30,195],"yield":[31],"guarantees":[33,51,84,155,165,192],"``for":[34],"free''.":[35],"In":[36],"this":[37],"work,":[38],"we":[39],"develop":[40],"unified":[42],"R\u00e9nyi":[43],"divergence":[44],"to":[46,97],"characterize":[47],"inherent":[49,153,190],"from":[54,113],"Bayesian":[56,99,185],"posterior":[57,72],"distribution.":[58],"We":[59,93],"show":[60],"that":[61],"loss":[64,176],"incurred":[65],"One-Posterior-Sampling":[67],"(OPS)":[68],"is":[69],"governed":[70],"exponential":[73,115],"moments":[74],"single-record":[77],"log-likelihood":[78],"ratio,":[79],"and":[80,117,145,179],"establish":[81],"explicit":[82],"under":[85],"uniformly":[86],"bounded,":[87],"sub-Gaussian,":[88],"or":[89,143],"sub-exponential":[90],"tail":[91],"regimes.":[92],"apply":[94],"representative":[98],"models,":[100],"including":[101],"categorical":[102],"likelihoods":[103],"with":[104,120,124,173],"arbitrary":[105],"priors,":[106],"Gaussian-Gaussian":[107],"conjugate":[108],"pair,":[109],"generalized":[110],"linear":[111,118],"models":[112,186],"family":[116],"regression":[119,129],"Gaussian":[121,125],"likelihood,":[122],"both":[123],"priors":[126],"on":[127],"coefficients.":[130],"Our":[131],"results":[132,160],"elucidate":[133],"sample":[134],"size,":[135],"model":[136],"structure,":[137],"neighboring":[138],"relations":[139],"in":[140],"(bounded":[142],"unbounded),":[144],"how":[146],"prior":[147],"if":[148],"applicable,":[149],"jointly":[150],"determine":[151],"OPS.":[157],"Furthermore,":[158],"our":[159],"recover":[161],"existing":[163],"OPS":[167,194],"special":[169],"cases":[170],"--":[171,178],"often":[172],"tighter":[174],"bounds":[177],"substantially":[180],"broaden":[181],"class":[183],"which":[188],"be":[196],"rigorously":[197],"characterized.":[198]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-16T00:00:00"}
