Mixture of Gaussian models and bayes error under differential privacy

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dc.authorid0000-0001-9795-9063
dc.authorid0000-0002-3149-1565
dc.contributor.authorXi, Boweien_US
dc.contributor.authorKantarcıoğlu, Muraten_US
dc.contributor.authorİnan, Alien_US
dc.date.accessioned2019-08-31T12:10:23Z
dc.date.accessioned2019-08-05T16:04:58Z
dc.date.available2019-08-31T12:10:23Z
dc.date.available2019-08-05T16:04:58Z
dc.date.issued2011
dc.departmentIşık Üniversitesi, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering, Department of Computer Engineeringen_US
dc.description.abstractGaussian mixture models are an important tool in Bayesian decision theory. In this study, we focus on building such models over statistical database protected under differential privacy. Our approach involves querying necessary statistics from a database and building a Bayesian classifier over the noise added responses generated according to differential privacy. We formally analyze the sensitivity of our query set. Since there are multiple methods to query a statistic, either directly or indirectly, we analyze the sensitivities for different querying methods. Furthermore we establish theoretical bounds for the Bayes error for the univariate (one dimensional) case. We study the Bayes error for the multivariate (high dimensional) case in experiments with both simulated data and real life data. We discover that adding Laplace noise to a statistic under certain constraint is problematic. For example variance-covariance matrix is no longer positive definite after noise addition. We propose a heuristic method to fix the noise added variance-covariance matrix.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationXi, B., Kantarcıoğlu, M. & İnan, A. (2011). Mixture of gaussian models and bayes error under differential privacy. Paper presented at the CODASPY'11 - Proceedings of the 1st ACM Conference on Data and Application Security and Privacy, 179-190. doi:10.1145/1943513.1943537en_US
dc.identifier.doi10.1145/1943513.1943537
dc.identifier.endpage189
dc.identifier.isbn9781450304665
dc.identifier.scopus2-s2.0-79952783992
dc.identifier.scopusqualityN/A
dc.identifier.startpage179
dc.identifier.urihttps://hdl.handle.net/11729/1947
dc.identifier.urihttps://dx.doi.org/10.1145/1943513.1943537
dc.indekslendigikaynakScopusen_US
dc.institutionauthorİnan, Alien_US
dc.institutionauthorid0000-0002-3149-1565
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.relation.ispartofCODASPY'11 - Proceedings of the 1st ACM Conference on Data and Application Security and Privacyen_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectClassificationen_US
dc.subjectDifferential privacyen_US
dc.subjectMixture modelsen_US
dc.subjectStatistical databasesen_US
dc.subjectGaussian Mixture Modelen_US
dc.subjectBayes erroren_US
dc.subjectBayesian classifieren_US
dc.subjectBayesian decision theoryen_US
dc.subjectDifferential privaciesen_US
dc.subjectHigh-dimensionalen_US
dc.subjectLaplace noiseen_US
dc.subjectMultiple methodsen_US
dc.subjectNoise additionen_US
dc.subjectPositive definiteen_US
dc.subjectReal life dataen_US
dc.subjectSimulated dataen_US
dc.subjectStatistical databaseen_US
dc.subjectTheoretical boundsen_US
dc.subjectUnivariateen_US
dc.subjectVariance-covariance matrixen_US
dc.subjectBayesian networksen_US
dc.subjectCovariance matrixen_US
dc.subjectDatabase systemsen_US
dc.subjectDecision theoryen_US
dc.subjectHeuristic methodsen_US
dc.subjectMixturesen_US
dc.subjectStatisticsen_US
dc.subjectData privacyen_US
dc.titleMixture of Gaussian models and bayes error under differential privacyen_US
dc.typeConference Objecten_US
dspace.entity.typePublication

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