Differential privacy for functions and functional data

By Rob Hall, Alessandro Rinaldo, Larry A. Wasserman. 2012

196 citations recorded by the source corpus.

Differential privacy is a rigorous cryptographically-motivated characterization of data privacy which may be applied when releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yields differential privacy. When the functions lie in the reproducing kernel Hilbert space (RKHS) generated by the covariance kernel of the Gaussian process, then the correct noise level is established by measuring the "sensitivity" of the function in the RKHS norm. As examples we consider kernel density estimation, kernel support vector machines, and functions in RKHSs.

Subfields: Artificial Intelligence, Sociology and Political Science

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Citations in the corpus

Differentially Private Data Publishing and Analysis: A Survey (2017, methodology): “By choosing different loss functions, ERM can be implemented for certain learning tasks, such as linear regression [69], in which the loss function is defined as maximum likelihood estimation (MLE); logistic regression [68], in which the loss function is defined as logistic loss; and the kernel meth”
Unlocking High-Accuracy Differentially Private Image Classification through Scale (2022, unknown): “More formally, if an algorithm is ( 𝜀, 𝛿 ) -DP then it must satisfy ln ( 1 − 𝛽 − 𝛿 ) ≤ 𝜀 (Hall et al., 2013), where 𝛼 and 𝛽 denote the Type I and Type II errors of the hypothesis testing procedure.”
Minimax Filter: Learning to Preserve Privacy from Inference Attacks (2016, background): “In particular, differential privacy can be defined for continuous and/or highdimensional attributes and for functions (Hall et al., 2013).”
Finite Sample Differentially Private Confidence Intervals (2017, background): “…there have been several works seeking the best asymptotic approximations we can obtain for population statistics under differential privacy, such as Dwork and Lei (2009); Smith (2011); Wasserman and Zhou (2010); Wasserman (2012); Hall et al. (2013); Duchi et al. (2013a,b); Barber and Duchi (2014).”
Differentially Private Learning with Kernels (2013, methodology): “Another relevant work is by Hall et al. (2012) that provides a method to release function values in RKHS in a differentially private manner.”
Differentially Private Distributed Convex Optimization via Functional Perturbation (2015, background): “In [13], the authors propose the addition of a sample path of a Gaussian random process to the objective function, but do not explore the generalization to arbitrary dimensions or ensure the smoothness and convexity of the resulting function.”
Toward Information Privacy for the Internet of Things: A Nonparametric Learning Approach (2018, background): “Achieving data privacy has been comprehensively addressed in [25], [38]–[41].”
A Survey on Internet of Things: Security and Privacy Issues (2014, methodology): “To ensure the output (typically aggregate queries) is independent of the absence or presence of a particular record adds noise called as differential privacy [14] could be the appropriate technique.”