Differentially Private Nonparametric Hypothesis Testing

By Simon Couch, Zeki Kazan, Kaiyan Shi, Andrew Bray, Adam Groce. 2019

52 citations recorded by the source corpus.

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met.

Subfields: Artificial Intelligence, Computer Science Applications, 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.”
Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms (2020, background): “, 2016], and in testing independence between a discrete and a continuous variable by constructing differentially private versions of classical rank-based tests [Couch et al., 2019].”
Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation (2019, background): “Mean estimation also naturally arises in hypothesis testing [33, 18, 7, 9, 10, 8].”
Differentially Private Confidence Intervals (2020, background): “As a result, the work on private hypothesis testing in this setting [4, 18] does not help us here.”