Mixture of Gaussian models and bayes error under differential privacy
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Dosyalar
Tarih
2011
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Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Gaussian 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.
Açıklama
Anahtar Kelimeler
Classification, Differential privacy, Mixture models, Statistical databases, Gaussian Mixture Model, Bayes error, Bayesian classifier, Bayesian decision theory, Differential privacies, High-dimensional, Laplace noise, Multiple methods, Noise addition, Positive definite, Real life data, Simulated data, Statistical database, Theoretical bounds, Univariate, Variance-covariance matrix, Bayesian networks, Covariance matrix, Database systems, Decision theory, Heuristic methods, Mixtures, Statistics, Data privacy
Kaynak
CODASPY'11 - Proceedings of the 1st ACM Conference on Data and Application Security and Privacy
WoS Q Değeri
Scopus Q Değeri
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Künye
Xi, 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:10.1145/1943513.1943537
