Estimating Sparse Discrete Distributions Under Local Privacy and Communication Constraints

TL;DR

This paper investigates the problem of estimating sparse discrete distributions while respecting local differential privacy and communication constraints, providing tight bounds and efficient schemes for both scenarios.

Contribution

It introduces new bounds on sample complexity and proposes practical schemes using Hadamard Response and hashing functions for privacy-preserving distribution estimation.

Findings

Sample complexity characterized up to a constant factor under LDP.

Sample complexity characterized up to a logarithmic factor under communication constraints.

Proposed schemes are efficient and near-optimal based on theoretical bounds.

Abstract

We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant factor and the sample complexity under communication constraints up to a logarithmic factor. Our upper bounds under LDP are based on the Hadamard Response, a private coin scheme that requires only one bit of communication per user. Under communication constraints, we propose public coin schemes based on random hashing functions. Our tight lower bounds are based on the recently proposed method of chi squared contractions.