The structure of optimal private tests for simple hypotheses

Canonne, Clément L.; Kamath, Gautam; McMillan, Audra; Smith, Adam; Ullman, Jonathan

doi:10.1145/3313276.3316336

Cited by 35 publications

(30 citation statements)

References 49 publications

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“…However, Brenner and Nissim (2014) showed that when the data are non-binary, there is no universal utility maximizing mechanism such as the staircase mechanism. As Canonne et al (2018) discuss, this result seems to imply that in settings where the data is non-binary, it may not be possible to develop DP-UMP tests.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…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%

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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: Discussion and Future Directionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Differentially Private Inference for Binomial Data

Awan

Slavković

2020

JPC

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“…Canonne et al [ 52 ] calculated the sample complexity bounds of an ε -differentially private test for distinguishing between two distributions. They also applied differentially private change-point detection.…”

Section: Related Workmentioning

confidence: 99%

Privacy-preserving chi-squared test of independence for small samples

Sei

Ohsuga

2021

BioData Mining

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Background The importance of privacy protection in analyses of personal data, such as genome-wide association studies (GWAS), has grown in recent years. GWAS focuses on identifying single-nucleotide polymorphisms (SNPs) associated with certain diseases such as cancer and diabetes, and the chi-squared (χ2) hypothesis test of independence can be utilized for this identification. However, recent studies have shown that publishing the results of χ2 tests of SNPs or personal data could lead to privacy violations. Several studies have proposed anonymization methods for χ2 testing with ε-differential privacy, which is the cryptographic community’s de facto privacy metric. However, existing methods can only be applied to 2×2 or 2×3 contingency tables, otherwise their accuracy is low for small numbers of samples. It is difficult to collect numerous high-sensitive samples in many cases such as COVID-19 analysis in its early propagation stage. Results We propose a novel anonymization method (RandChiDist), which anonymizes χ2 testing for small samples. We prove that RandChiDist satisfies differential privacy. We also experimentally evaluate its analysis using synthetic datasets and real two genomic datasets. RandChiDist achieved the least number of Type II errors among existing and baseline methods that can control the ratio of Type I errors. Conclusions We propose a new differentially private method, named RandChiDist, for anonymizing χ2 values for an I×J contingency table with a small number of samples. The experimental results show that RandChiDist outperforms existing methods for small numbers of samples.

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“…The maximal-leakage setting inverts this goal, and protects the observed values while maximizing the detection of hypotheses on the distributions. This distinction in goal also applies with respect to the distributional privacy framework [2] and in the explorations of [3] into general privatized hypothesis testing.…”

Section: Related Work and Related Privacy Definitionsmentioning

confidence: 99%

Profile-based Privacy for Locally Private Computations

Geumlek

Chaudhuri

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Differential privacy has emerged as a gold standard in privacy-preserving data analysis. A popular variant is local differential privacy, where the data holder is the trusted curator. A major barrier, however, towards a wider adoption of this model is that it offers a poor privacy-utility trade-off.In this work, we address this problem by introducing a new variant of local privacy called profilebased privacy. The central idea is that the problem setting comes with a graph G of data generating distributions, whose edges encode sensitive pairs of distributions that should be made indistinguishable. This provides higher utility because unlike local differential privacy, we no longer need to make every pair of private values in the domain indistinguishable, and instead only protect the identity of the underlying distribution. We establish privacy properties of the profile-based privacy definition, such as post-processing invariance and graceful composition. Finally, we provide mechanisms that are private in this framework, and show via simulations that they achieve higher utility than the corresponding local differential privacy mechanisms.

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The structure of optimal private tests for simple hypotheses

Cited by 35 publications

References 49 publications

Differentially Private Inference for Binomial Data

Differentially Private Inference for Binomial Data

Privacy-preserving chi-squared test of independence for small samples

Profile-based Privacy for Locally Private Computations

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