Local Private Hypothesis Testing: Chi-Square Tests

By Marco Gaboardi, Ryan M. Rogers. 2017

64 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Sociology and Political Science

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Citations in the corpus

The structure of optimal private tests for simple hypotheses (2018, background): “Another related area [1, 41, 66] studies hypothesis testing in the local model of differential privacy.”
Collecting and Analyzing Multidimensional Data with Local Differential Privacy (2019, background): “Various data analytics and machine learning problems have been studied under LDP, such as probability distribution estimation [15], [23], [30], [32], [42], heavy hitter discovery [4], [7], [33], [39], frequent new term discovery [37], frequency estimation [5], [38], frequent itemset mining [40], mar”
Communication Complexity in Locally Private Distribution Estimation and Heavy Hitters (2019, background): “The complementary problem of hypothesis testing has also been studied in the locally differentially private setting in [39, 40, 41], where the goal is to test whether the data samples are generated from one class of distributions or another.”
Locally Private Mean Estimation: Z-test and Tight Confidence Intervals (2018, background): “Karwa and Vadhan (2018) give matching upper- and lower-bounds on the confidence intervals for the mean of a population, also in the centralized model.”
Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms (2020, methodology): “The goodness-of-ﬁt testing problem, which we consider in this paper, was investigated in Gaboardi and Rogers [2017], Sheﬀet [2018], where the authors provide analyses of procedures based on chi-squared tests and the optimal non-private test of Valiant and Valiant [2017], respectively, under speciﬁc…”
Differentially Private Uniformly Most Powerful Tests for Binomial Data (2018, background): “Gaboardi and Rogers (2017) work under “Local Differential Privacy”, a stronger notion of privacy than DP, and develop multinomial tests based on asymptotic distributions.”
Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit (2019, methodology): “The testing counterpart, speciﬁcally identity testing, was studied in the locally differentially private (LDP) setting by Gaboardi and Rogers [GR18] and Sheffet [She18], followed by [ACFT19]; and in the communication-constrained setting in [ACT19c, ACT19b], as well as by (with a slightly different…”
Locally Private Gaussian Estimation (2018, background): “In local differential privacy, several recent works have studied related statistical tasks like identity and independence testing [2, 17, 24], albeit restricted to discrete distributions.”
Calibrate: Frequency Estimation and Heavy Hitter Identification with Local Differential Privacy via Incorporating Prior Knowledge (2018, background): “Moreover, hypothesis testing with LDP [17] can also help to determine the distribution family of the true item frequencies.”
Test without Trust: Optimal Locally Private Distribution Testing (2018, background): “We remark at the outset that the problems studied here have been considered earlier in [31, 22].”
Differentially Private Assouad, Fano, and Le Cam (2020, methodology): “Several estimation tasks have also been considered under the distributed notion of local diﬀerential privacy, e.g., [War65, KLN + 11, EPK14, DJW13, KBR16, WHW + 16, YB18, GR18, ACT19, ASZ19, AS19, ACFT19, She17].”
Privately Learning High-Dimensional Distributions (2018, background): “, 2012; Gaboardi et al., 2016a). When the distribution is low-dimensional, there are many more effective algorithms that avoid the polynomial dependence on the size of the range. For example, in the setting above of estimating a single univariate Gaussian, Karwa and Vadhan (2018) showed how to estim”
Inference Under Information Constraints III: Local Privacy Constraints (2021, background): “The works most closely related to ours are those that consider distribution testing under LDP constraints [1], [3], [4], [5], [12], [17], [32], [42].”
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.”