Differentially Private Nonparametric Hypothesis Testing

Couch, Simon; Kazan, Zeki; Shi, Kaiyan; Bray, Andrew M.; Groce, Adam

doi:10.48550/arxiv.1903.09364

Cited by 2 publications

(3 citation statements)

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“…One of our main findings -that robust estimators perform better than parametric estimators in the differentially private setting, even when the data come from a parametric model -corroborate insights by [16] with regard to the connection between robust statistics and differential privacy, and by [14] in the context of hypothesis testing.…”

Section: Other Related Worksupporting

confidence: 72%

Differentially Private Simple Linear Regression

Alabi¹,

McMillan

Sarathy³

et al. 2022

Proceedings on Privacy Enhancing Technologies

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Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal sensitive individual information. We study regression algorithms that satisfy differential privacy, a constraint which guarantees that an algorithm’s output reveals little about any individual input data record, even to an attacker with side information about the dataset. Motivated by the Opportunity Atlas, a high-profile, small-area analysis tool in economics research, we perform a thorough experimental evaluation of differentially private algorithms for simple linear regression on small datasets with tens to hundreds of records—a particularly challenging regime for differential privacy. In contrast, prior work on differentially private linear regression focused on multivariate linear regression on large datasets or asymptotic analysis. Through a range of experiments, we identify key factors that affect the relative performance of the algorithms. We find that algorithms based on robust estimators—in particular, the median-based estimator of Theil and Sen—perform best on small datasets (e.g., hundreds of datapoints), while algorithms based on Ordinary Least Squares or Gradient Descent perform better for large datasets. However, we also discuss regimes in which this general finding does not hold. Notably, the differentially private analogues of Theil–Sen (one of which was suggested in a theoretical work of Dwork and Lei) have not been studied in any prior experimental work on differentially private linear regression.

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Section: Other Related Worksupporting

confidence: 72%

Differentially Private Simple Linear Regression

Alabi¹,

McMillan

Sarathy³

et al. 2022

Proceedings on Privacy Enhancing Technologies

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“…Figure 7 in Appendix D shows that these findings are generally consistent across choices of ε. 4 As a rule of thumb, we find that SYMQ is the superior algorithm once n > 100/ε.…”

Section: New Algorithmsmentioning

confidence: 85%

“…But private hypothesis testing algorithms give a p-value at one point and cannot be run repeatedly without losing privacy, so there is no way to find where the cutoff for rejecting would be. As a result, the work on private hypothesis testing in this setting [4,18] does not help us here.…”

Section: Private Confidence Intervalsmentioning

confidence: 99%

Differentially Private Confidence Intervals

Du,

Foot,

Moniot

et al. 2020

Preprint

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Confidence intervals for the population mean of normally distributed data are some of the most standard statistical outputs one might want from a database. In this work we give practical differentially private algorithms for this task. We provide five algorithms and then compare them to each other and to prior work. We give concrete, experimental analysis of their accuracy and find that our algorithms provide much more accurate confidence intervals than prior work. For example, in one setting (with = 0.1 and n = 2782) our algorithm yields an interval that is only 1/15 th the size of the standard set by prior work.

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Differentially Private Nonparametric Hypothesis Testing

Cited by 2 publications

References 0 publications

Differentially Private Simple Linear Regression

Differentially Private Simple Linear Regression

Differentially Private Confidence Intervals

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