Local Private Hypothesis Testing: Chi-Square Tests

TL;DR

This paper investigates the design and analysis of chi-square hypothesis tests under local differential privacy, focusing on goodness of fit and independence testing without trusted data aggregators.

Contribution

It introduces locally private chi-square tests for goodness of fit and independence, adapting traditional methods to the local privacy setting.

Findings

Proposed new locally private chi-square test procedures.

Analyzed the privacy-utility trade-offs in local differential privacy.

Provided theoretical guarantees for the tests' accuracy.

Abstract

The local model for differential privacy is emerging as the reference model for practical applications collecting and sharing sensitive information while satisfying strong privacy guarantees. In the local model, there is no trusted entity which is allowed to have each individual's raw data as is assumed in the traditional curator model for differential privacy. So, individuals' data are usually perturbed before sharing them. We explore the design of private hypothesis tests in the local model, where each data entry is perturbed to ensure the privacy of each participant. Specifically, we analyze locally private chi-square tests for goodness of fit and independence testing, which have been studied in the traditional, curator model for differential privacy.