Estimating Sparse Discrete Distributions Under Local Privacy and Communication Constraints
This work addresses privacy-preserving data analysis for distributed systems, providing theoretical guarantees for sparse distribution estimation, but it is incremental as it builds on existing methods like chi squared contractions.
The paper tackles the problem of estimating sparse discrete distributions under local differential privacy and communication constraints, characterizing sample complexity up to constant factors for LDP and logarithmic factors for communication constraints, with upper bounds using Hadamard Response and random hashing schemes.
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.