Efficient, Differentially Private Point Estimators

By Adam D. Smith. 2008

80 citations recorded by the source corpus.

Differential privacy is a recent notion of privacy for statistical databases that provides rigorous, meaningful confidentiality guarantees, even in the presence of an attacker with access to arbitrary side information. We show that for a large class of parametric probability models, one can construct a differentially private estimator whose distribution converges to that of the maximum likelihood estimator. In particular, it is efficient and asymptotically unbiased. This result provides (further) compelling evidence that rigorous notions of privacy in statistical databases can be consistent with statistically valid inference.

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Citations in the corpus

Learning Anonymized Representations with Adversarial Neural Networks (2018, background): “From a statistical perspective, convergence rates for minimax risk for problems in which the data must be kept conﬁdential even from the February 27, 2018 DRAFT learner have been reported in [Smith, 2008] and [Duchi et al., 2014].”
Distributed Private Data Analysis: On Simultaneously Solving How and What (2008, background): “... of recent works [7, 15, 14, 2, 11, 8, 9]. It has been demonstrated that differentially private analyses exist for a variety of tasks including the approximation of numerical functions (by adding carefully chosen random noise that conceals any single individual’s contribution) [11, 2, 22, 17], no”
Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (2015, background): “The idea is to simply privately release an estimate of the gradient (as in Song et al. (2013); Bassily et al.”
Differentially Private Nonparametric Hypothesis Testing (2019, background): “One area of research is the study of the rate of convergence of private statistics to the distributions of their public analogues [25, 26, 34].”
Random Differential Privacy (2011, background): “, statistical point estimators [15] and regularized logistic regression estimates [4].”
Differential privacy based on importance weighting (2013, background): “Some of them answer unrestricted queries without publishing data (Smith 2008; McSherry and Mironov 2009; Li et al. 2010; McSherry and Mahajan 2010; Rastogi and Nath 2010).”
Probabilistic Inference and Differential Privacy (2010, background): “Much of the existing statistical literature is concerned with identifying cases when the differentially-private observations are “as good” as traditional statistical estimators, in terms of efficiency [1], power [2], and minimax rates [3], and also robust estimators [4].”
Differential Privacy for Clinical Trial Data: Preliminary Evaluations (2009, methodology): “We als o modify the Laplace noise formula given in [11] by removing one of the parameters such that given a fixed sample size N , we only need to adjust the differential privacy level ǫ to allow for trade-off between the privacy and the asymptotic proper ties of the returned estimators.”
The price of privately releasing contingency tables and the spectra of random matrices with correlated rows (2010, background): “rule of thumb, then, is that the distortion interferes seriously when it is not o( √ n) [12, 3, 31 ].”
Differentially Private Bayesian Linear Regression (2019, background): “…(OPS) [Dimitrakakis et al., 2014, Geumlek et al., 2017, Minami et al., 2016, Wang, 2018, Wang et al., 2015, Zhang et al., 2016], subsample and aggregate [Dwork and Smith, 2010, Smith, 2008], objective perturbation [Kifer et al., 2012], and noisy stochastic gradient descent [Bassily et al., 2014].”
Multiparty Differential Privacy via Aggregation of Locally Trained Classifiers (2010, methodology): “Similar to [10], we choose a simple average as the aggregation function and the parties together release the perturbed aggregate classifier which satisfies differential privacy.”
Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation (2019, methodology): “Smith [32] gives a general method for private point estimation, with asymptotic efficiency guarantees for general “asymptotically normal” estimators.”
Differential privacy and robust statistics (2009, methodology): “In parallel with our eorts, Smith [ 16 ] showed that for well-behaved parametric probability models one can construct an ecient (in the statistical sense) and unbiased estimator whose distribution converges to that of the maximum likelihood estimator.”
Per-instance Differential Privacy and the Adaptivity of Posterior Sampling in Linear and Ridge regression (2017, background): “Secondly, both [17] and [28] suffer from additional polynomial dependence on the dimension in the supposedly lower order term, and that affects finite sample performance.”
Differential Privacy and Machine Learning: a Survey and Review (2014, background): “[49, 50] give a differentially private mechanism for point estimation.”