Private Estimation when Data and Privacy Demands are Correlated

TL;DR

This paper develops algorithms for private data estimation that handle heterogeneous privacy demands, especially when privacy needs are correlated with data, achieving near-optimal performance with theoretical guarantees and empirical validation.

Contribution

It introduces novel algorithms for empirical mean and frequency estimation under correlated privacy constraints, extending differential privacy to heterogeneous and worst-case datasets.

Findings

Algorithms achieve minimax optimality in several settings.

Proposed methods outperform baseline techniques in experiments.

Theoretical guarantees hold under different privacy-data correlation scenarios.

Abstract

Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We consider the problems of empirical mean estimation for univariate data and frequency estimation for categorical data, both subject to heterogeneous privacy constraints. Each user, contributing a sample to the dataset, is allowed to have a different privacy demand. The dataset itself is assumed to be worst-case and we study both problems under two different formulations -- first, where privacy demands and data may be correlated, and second, where correlations are weakened by random permutation of the dataset. We establish theoretical performance guarantees for our proposed algorithms, under both PAC error and mean-squared error. These performance guarantees translate to minimax optimality in several instances, and experiments confirm superior performance of our algorithms over other baseline techniques.