Communication Complexity in Locally Private Distribution Estimation and Heavy Hitters
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We consider the problems of distribution estimation and heavy hitter (frequency) estimation under privacy and communication constraints. While these constraints have been studied separately, optimal schemes for one are sub-optimal for the other. We propose a sample-optimal ε-locally differentially private (LDP) scheme for distribution estimation, where each user communicates only one bit, and requires no public randomness. We show that Hadamard Response, a recently proposed scheme for ε-LDP distribution estimation is also utility-optimal for heavy hitter estimation. Finally, we show that unlike distribution estimation, without public randomness where only one bit suffices, any heavy hitter estimation algorithm that communicates o({ n, k}) bits from each user cannot be optimal.
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