
The Role of Interactivity in Local Differential Privacy
We study the power of interactivity in local differential privacy. First...
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Private Hypothesis Selection
We provide a differentially private algorithm for hypothesis selection. ...
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Linear Queries Estimation with Local Differential Privacy
We study the problem of estimating a set of d linear queries with respec...
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Learning discrete distributions: user vs itemlevel privacy
Much of the literature on differential privacy focuses on itemlevel pri...
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Locally private nonasymptotic testing of discrete distributions is faster using interactive mechanisms
We find separation rates for testing multinomial or more general discret...
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Learning without Interaction Requires Separation
One of the key resources in largescale learning systems is the number o...
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Comparing Population Means under Local Differential Privacy: with Significance and Power
A statistical hypothesis test determines whether a hypothesis should be ...
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Locally Private Hypothesis Selection
We initiate the study of hypothesis selection under local differential privacy. Given samples from an unknown probability distribution p and a set of k probability distributions Q, we aim to output, under the constraints of εlocal differential privacy, a distribution from Q whose total variation distance to p is comparable to the best such distribution. This is a generalization of the classic problem of kwise simple hypothesis testing, which corresponds to when p ∈Q, and we wish to identify p. Absent privacy constraints, this problem requires O(log k) samples from p, and it was recently shown that the same complexity is achievable under (central) differential privacy. However, the naive approach to this problem under local differential privacy would require Õ(k^2) samples. We first show that the constraint of local differential privacy incurs an exponential increase in cost: any algorithm for this problem requires at least Ω(k) samples. Second, for the special case of kwise simple hypothesis testing, we provide a noninteractive algorithm which nearly matches this bound, requiring Õ(k) samples. Finally, we provide sequentially interactive algorithms for the general case, requiring Õ(k) samples and only O(loglog k) rounds of interactivity. Our algorithms are achieved through a reduction to maximum selection with adversarial comparators, a problem of independent interest for which we initiate study in the parallel setting. For this problem, we provide a family of algorithms for each number of allowed rounds of interaction t, as well as lower bounds showing that they are nearoptimal for every t. Notably, our algorithms result in exponential improvements on the round complexity of previous methods.
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