### 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 language | English (US) |
---|---|

Pages (from-to) | 4208-4218 |

Number of pages | 11 |

Journal | Advances in Neural Information Processing Systems |

Volume | 2018-December |

State | Published - Jan 1 2018 |

Event | 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: Dec 2 2018 → Dec 8 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*Advances in Neural Information Processing Systems*,

*2018-December*, 4208-4218.

}

*Advances in Neural Information Processing Systems*, vol. 2018-December, pp. 4208-4218.

**Differentially private uniformly most powerful tests for binomial data.** / Awan, Jordan; Slavkovic, Aleksandra B.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Differentially private uniformly most powerful tests for binomial data

AU - Awan, Jordan

AU - Slavkovic, Aleksandra B.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85064832271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064832271&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85064832271

VL - 2018-December

SP - 4208

EP - 4218

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

ER -