Statistical Approximating Distributions Under Differential Privacy

Wang, Yue; Kifer, Daniel; Lee, Jae Woo; Karwa, Vishesh

doi:10.29012/jpc.666

Cited by 16 publications

(16 citation statements)

References 25 publications

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“…Given a DP output, Sheffet (2017) and Barrientos et al (2017) develop significance tests for regression coefficients. Following a common strategy in the field of Statistics, Wang et al (2018) develop approximating distributions for DP statistics, which can be used to construct hypothesis tests and confidence intervals. In a recent work, Canonne et al (2018) show that for simple hypothesis tests, a DP test based on a clamped likelihood ratio test achieves optimal sample complexity.…”

Section: Introductionmentioning

confidence: 99%

Differentially Private Inference for Binomial Data

Awan

Slavković

2020

JPC

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We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests can be written in terms of linear constraints, and for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a 'Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. Our tests can also be stated as a post-processing of a random variable, whose distribution we coin "Truncated-Uniform-Laplace" (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact p-values, which are easily computed in terms of the Tulap random variable.Using the above techniques, we show that our tests can be applied to give uniformly most accurate one-sided confidence intervals and optimal confidence distributions. We also derive uniformly most powerful unbiased (UMPU) two-sided tests, which lead to uniformly most accurate unbiased (UMAU) two-sided confidence intervals. We show that our results can be applied to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that all our tests have exact type I error, and are more powerful than current techniques.

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Section: Introductionmentioning

confidence: 99%

Differentially Private Inference for Binomial Data

Awan

Slavković

2020

JPC

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“…Smith, 2011;. Even though in these settings, the noise is asymptotically negligible, developing accurate approximations is still a challenge, which Wang et al (2018) recently tackled.…”

Section: Exponential Mechanismmentioning

confidence: 99%

Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA

Awan,

Kenney,

Reimherr

et al. 2019

Preprint

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The exponential mechanism is a fundamental tool of Differential Privacy (DP) due to its strong privacy guarantees and flexibility. We study its extension to settings with summaries based on infinite dimensional outputs such as with functional data analysis, shape analysis, and nonparametric statistics. We show that one can design the mechanism with respect to a specific base measure over the output space, such as a Guassian process. We provide a positive result that establishes a Central Limit Theorem for the exponential mechanism quite broadly. We also provide an apparent negative result, showing that the magnitude of the noise introduced for privacy is asymptotically non-negligible relative to the statistical estimation error. We develop an -DP mechanism for functional principal component analysis, applicable in separable Hilbert spaces. We demonstrate its performance via simulations and applications to two datasets.

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“…These approximations, however, need to be adjusted when the underlying data are perturbed by DP. Wang et al (2018) lay out how to generate valid approximating distributions for differentially private statistics.…”

Section: Articles In This Issuementioning

confidence: 99%