A New Class of Private Chi-Square Tests

By Daniel Kifer, Ryan M. Rogers. 2016

27 citations recorded by the source corpus.

In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of the classical (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.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering, Statistics and Probability

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Citations in the corpus

The structure of optimal private tests for simple hypotheses (2018, background): “One line of work [17, 21, 40, 44, 49, 71, 76] designs differentially private versions of popular test statistics for testing goodness-of-fit, closeness, and independence, as well as private ANOVA, focusing on the performance at small sample sizes.”
Differentially Private Identity and Equivalence Testing of Discrete Distributions (2018, background): “The majority of these works (Wang et al., 2015; Gaboardi et al., 2016; Kifer & Rogers, 2017) only obtain type I error guarantees subject to the privacy constraint, which is a significantly weaker guarantee than ours.”
Privately Learning High-Dimensional Distributions (2018, unknown): “For example, [WLK15, GLRV16, KR17, CDK17, KSF17] gave private algorithms for goodness-of-ﬁt testing, closeness, and independence testing.”
INSPECTRE: Privately Estimating the Unseen (2018, background): “Other works investigating private hypothesis testing include [WLK15, GLRV16, KR17, KSF17, Rog17, GR17], which focus less on characterizing the ﬁnite-sample guarantees of such tests, and more on understanding their asymptotic properties and applications to computing p-values.”
Inference Under Information Constraints III: Local Privacy Constraints (2021, background): “Independence testing under differentially privacy has been studied in [31], [40], [47] and the first algorithm with finite sample guarantee was given in [10].”
Test without Trust: Optimal Locally Private Distribution Testing (2018, methodology): “Here the algorithm itself is run by a trusted curator who has access to all the user data, but needs to ensure that the output of the test maintains differential privacy; see [21, 28, 33] for a sampling of results on identity and independence testing.”
Differentially Private Identity and Closeness Testing of Discrete Distributions (2017, background): “A recent line of work [27, 18, 21, 5] has studied distribution testing with privacy constraints.”
Finite Sample Differentially Private Confidence Intervals (2017, methodology): “Kifer and Rogers (2016) analyze their hypothesis tests using asymptotics that constrain the setting of the privacy parameter in terms of the sample size n (e.g. ǫ ≥ Ω(1/√n)), but it’s not clear that this relationship is safe to assume in general.”