Discrete Distribution Estimation under Local Privacy

TL;DR

This paper introduces new mechanisms for estimating discrete distributions under local privacy, achieving improved utility and theoretical optimality across privacy levels, thus enhancing privacy-preserving data collection.

Contribution

It proposes the hashed K-ary Randomized Response mechanism and establishes its order-optimality, advancing the state-of-the-art in local privacy distribution estimation.

Findings

KRR mechanism outperforms existing methods in utility

Theoretical analysis confirms order-optimality of KRR and RAPPOR

Empirical results demonstrate practical effectiveness across privacy regimes

Abstract

The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting the underlying data. We present new mechanisms, including hashed K-ary Randomized Response (KRR), that empirically meet or exceed the utility of existing mechanisms at all privacy levels. New theoretical results demonstrate the order-optimality of KRR and the existing RAPPOR mechanism at different privacy regimes.