A New Class of Private Chi-Square Hypothesis Tests

Ryan Rogers, Daniel Kifer
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:991-1000, 2017.

Abstract

In this paper, we develop new test statistics for hypothesis testing over differentially private data. These statistics are designed specifically so that their asymptotic distributions, after accounting for privacy noise, match the asymptotics of the non-private chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness-of-fit and independence testing). Empirically, these new test statistics outperform prior work, which focused on noisy versions of existing statistics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-rogers17a, title = {{A New Class of Private Chi-Square Hypothesis Tests}}, author = {Rogers, Ryan and Kifer, Daniel}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {991--1000}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/rogers17a/rogers17a.pdf}, url = {https://proceedings.mlr.press/v54/rogers17a.html}, abstract = {In this paper, we develop new test statistics for hypothesis testing over differentially private data. These statistics are designed specifically so that their asymptotic distributions, after accounting for privacy noise, match the asymptotics of the non-private chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness-of-fit and independence testing). Empirically, these new test statistics outperform prior work, which focused on noisy versions of existing statistics.} }
Endnote
%0 Conference Paper %T A New Class of Private Chi-Square Hypothesis Tests %A Ryan Rogers %A Daniel Kifer %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-rogers17a %I PMLR %P 991--1000 %U https://proceedings.mlr.press/v54/rogers17a.html %V 54 %X In this paper, we develop new test statistics for hypothesis testing over differentially private data. These statistics are designed specifically so that their asymptotic distributions, after accounting for privacy noise, match the asymptotics of the non-private chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness-of-fit and independence testing). Empirically, these new test statistics outperform prior work, which focused on noisy versions of existing statistics.
APA
Rogers, R. & Kifer, D.. (2017). A New Class of Private Chi-Square Hypothesis Tests. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:991-1000 Available from https://proceedings.mlr.press/v54/rogers17a.html.

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