Privacy and Statistical Risk: Formalisms and Minimax Bounds

By Rina Foygel Barber, John C. Duchi. 2014

106 citations recorded by the source corpus.

We explore and compare a variety of definitions for privacy and disclosure limitation in statistical estimation and data analysis, including (approximate) differential privacy, testing-based definitions of privacy, and posterior guarantees on disclosure risk. We give equivalence results between the definitions, shedding light on the relationships between different formalisms for privacy. We also take an inferential perspective, where---building off of these definitions---we provide minimax risk bounds for several estimation problems, including mean estimation, estimation of the support of a distribution, and nonparametric density estimation. These bounds highlight the statistical consequences of different definitions of privacy and provide a second lens for evaluating the advantages and disadvantages of different techniques for disclosure limitation.

Subfields: Artificial Intelligence, Management Science and Operations Research

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Citations in the corpus

Protection Against Reconstruction and Its Applications in Private Federated Learning (2018, methodology): “First, these weakenings can never actually protect against a reconstruction breach for all possible observations z (Deﬁnition 2.1)— they can only protect conditional on the observation z lying in some appropriately high probability set (cf. [13, Thm. 1]).”
Extremal Mechanisms for Local Differential Privacy (2014, background): “Such tradeoffs also provide tools for comparing various notions of privacy (Barber and Duchi, 2014).”
Finite Sample Differentially Private Confidence Intervals (2017, background): “(2013a,b); Barber and Duchi (2014). 1.5 Conservative Statistical Inference with DP The works discussed in the previous section focus on providing point estimates for population quantities, but as mentioned earlier, it is also important to be able to provide measures of statistical significance, to p”
Differentially Private Assouad, Fano, and Le Cam (2020, methodology): “Fingerprinting (Steinke and Ullman, 2015; Bun et al., 2015; Dwork et al., 2015; Steinke and Ullman, 2017a; Bun et al., 2017, 2018; Kamath et al., 2019; Cai et al., 2019) is a versatile lower bounding method for (ε, δ)-DP for δ = O(1/n). It has been used to prove lower bounds for several problems, in”
Per-instance Differential Privacy and the Adaptivity of Posterior Sampling in Linear and Ridge regression (2017, background): “…Q ) A only Rényi-DP[24] sup Z sup z D α ( P (cid:107) Q ) A only Personal-DP[15, 20] sup Z ﬁxed z D δ ∞ ( P (cid:107) Q ) A and z TV-privacy[2] sup Z sup z P − Q (cid:107) TV A only KL-privacy[2] sup Z sup z D KL ( P (cid:107) Q ) A only On-Avg KL-privacy[32] Table 1: Comparing variances…”
Element Level Differential Privacy: The Right Granularity of Privacy (2019, unknown): “…the relative sample size necessary for private algorithms to achieve similar utility to that of non-private algorithms grows with problem dimension and inversely with the privacy parameter ε [Barber and Duchi 2014, Steinke and Ullman 2017, Duchi, Jordan, and Wainwright 2018, Duchi and Rogers 2019].”