Differentially private uniformly most powerful tests for binomial data

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

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. We show that our results also apply to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that our tests have exact type I error, and are more powerful than current techniques.

Original languageEnglish (US)
Pages (from-to)4208-4218
Number of pages11
JournalAdvances in Neural Information Processing Systems
Volume2018-December
StatePublished - Jan 1 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

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Random variables
Processing

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

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title = "Differentially private uniformly most powerful tests for binomial data",
abstract = "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. We show that our results also apply to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that our tests have exact type I error, and are more powerful than current techniques.",
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Differentially private uniformly most powerful tests for binomial data. / Awan, Jordan; Slavkovic, Aleksandra B.

In: Advances in Neural Information Processing Systems, Vol. 2018-December, 01.01.2018, p. 4208-4218.

Research output: Contribution to journalConference article

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