Differentially Private Inference for Binomial Data
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 e...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Labor Dynamics Institute
2020-01-01
|
| Series: | The Journal of Privacy and Confidentiality |
| Subjects: | |
| Online Access: | https://journalprivacyconfidentiality.org/index.php/jpc/article/view/725 |
| _version_ | 1818527922989826048 |
|---|---|
| author | Jordan Alexander Awan Aleksandra Slavkovic |
| author_facet | Jordan Alexander Awan Aleksandra Slavkovic |
| author_sort | Jordan Alexander Awan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T06:42:46Z |
| format | Article |
| id | doaj.art-c91415d4f64740f59d8e79e855a18cce |
| institution | Directory Open Access Journal |
| issn | 2575-8527 |
| language | English |
| last_indexed | 2024-12-11T06:42:46Z |
| publishDate | 2020-01-01 |
| publisher | Labor Dynamics Institute |
| record_format | Article |
| series | The Journal of Privacy and Confidentiality |
| spelling | doaj.art-c91415d4f64740f59d8e79e855a18cce2022-12-22T01:17:10ZengLabor Dynamics InstituteThe Journal of Privacy and Confidentiality2575-85272020-01-0110110.29012/jpc.725Differentially Private Inference for Binomial DataJordan Alexander Awan0Aleksandra Slavkovic1Pennsylvania State UniversityPennsylvania State UniversityWe 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.https://journalprivacyconfidentiality.org/index.php/jpc/article/view/725BernoulliHypothesis TestConfidence intervalFrequentistStatistical disclosure controlNeyman-Pearson |
| spellingShingle | Jordan Alexander Awan Aleksandra Slavkovic Differentially Private Inference for Binomial Data The Journal of Privacy and Confidentiality Bernoulli Hypothesis Test Confidence interval Frequentist Statistical disclosure control Neyman-Pearson |
| title | Differentially Private Inference for Binomial Data |
| title_full | Differentially Private Inference for Binomial Data |
| title_fullStr | Differentially Private Inference for Binomial Data |
| title_full_unstemmed | Differentially Private Inference for Binomial Data |
| title_short | Differentially Private Inference for Binomial Data |
| title_sort | differentially private inference for binomial data |
| topic | Bernoulli Hypothesis Test Confidence interval Frequentist Statistical disclosure control Neyman-Pearson |
| url | https://journalprivacyconfidentiality.org/index.php/jpc/article/view/725 |
| work_keys_str_mv | AT jordanalexanderawan differentiallyprivateinferenceforbinomialdata AT aleksandraslavkovic differentiallyprivateinferenceforbinomialdata |