
Locally Private Hypothesis Selection
We initiate the study of hypothesis selection under local differential p...
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Exponential Separations in Local Differential Privacy Through Communication Complexity
We prove a general connection between the communication complexity of tw...
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Classification in a Large Network
We construct and analyze the communication cost of protocols (interactiv...
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Interactive Inference under Information Constraints
We consider distributed inference using sequentially interactive protoco...
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Goodnessoffit testing for Hölder continuous densities under local differential privacy
We address the problem of goodnessoffit testing for Hölder continuous ...
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The Structure of Optimal Private Tests for Simple Hypotheses
Hypothesis testing plays a central role in statistical inference, and is...
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Interactive versus noninteractive locally, differentially private estimation: Two elbows for the quadratic functional
Local differential privacy has recently received increasing attention fr...
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The Role of Interactivity in Local Differential Privacy
We study the power of interactivity in local differential privacy. First, we focus on the difference between fully interactive and sequentially interactive protocols. Sequentially interactive protocols may query users adaptively in sequence, but they cannot return to previously queried users. The vast majority of existing lower bounds for local differential privacy apply only to sequentially interactive protocols, and before this paper it was not known whether fully interactive protocols were more powerful. We resolve this question. First, we classify locally private protocols by their compositionality, the multiplicative factor k ≥ 1 by which the sum of a protocol's singleround privacy parameters exceeds its overall privacy guarantee. We then show how to efficiently transform any fully interactive kcompositional protocol into an equivalent sequentially interactive protocol with an O(k) blowup in sample complexity. Next, we show that our reduction is tight by exhibiting a family of problems such that for any k, there is a fully interactive kcompositional protocol which solves the problem, while no sequentially interactive protocol can solve the problem without at least an Ω̃(k) factor more examples. We then turn our attention to hypothesis testing problems. We show that for a large class of compound hypothesis testing problems  which include all simple hypothesis testing problems as a special case  a simple noninteractive test is optimal among the class of all (possibly fully interactive) tests.
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