Estimating Sparse Discrete Distributions Under Local Privacy and Communication Constraints

By Jayadev Acharya, Yuhan Liu, Ziteng Sun. 2020

5 citations recorded by the source corpus.

We consider the task of estimating sparse discrete distributions under local differential privacy and communication constraints. Under local privacy constraints, we present a sample-optimal private-coin scheme that only sends a one-bit message per user. For communication constraints, we present a public-coin scheme based on random hashing functions, which we prove is optimal up to logarithmic factors. Our results show that the sample complexity only depends logarithmically on the ambient dimension, thus providing significant improvement in sample complexity under sparsity assumptions. Our lower bounds are based on a recently proposed chi-squared contraction method.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Electrical and Electronic Engineering

In Statistics and Probability

Citations in the corpus

Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints (2021, methodology): “For the estimation phase, we adopt a scheme similar to (Acharya et al., 2021), where each client encodes their local observation via an independent b-bit random hash function4 hi : [d] → [2b] as described in Algorithm 2.”