3,350 research outputs found
Differentially Private Nonparametric Hypothesis Testing
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
Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation
Motivated by growing concerns over ensuring privacy on social networks, we
develop new algorithms and impossibility results for fitting complex
statistical models to network data subject to rigorous privacy guarantees. We
consider the so-called node-differentially private algorithms, which compute
information about a graph or network while provably revealing almost no
information about the presence or absence of a particular node in the graph.
We provide new algorithms for node-differentially private estimation for a
popular and expressive family of network models: stochastic block models and
their generalization, graphons. Our algorithms improve on prior work, reducing
their error quadratically and matching, in many regimes, the optimal nonprivate
algorithm. We also show that for the simplest random graph models ( and
), node-private algorithms can be qualitatively more accurate than for
more complex models---converging at a rate of
instead of . This result uses a new extension lemma
for differentially private algorithms that we hope will be broadly useful
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