Utility Analysis and Enhancement of LDP Mechanisms in High-Dimensional Space

TL;DR

This paper introduces an analytical framework to evaluate and improve the utility of local differential privacy mechanisms in high-dimensional data collection, demonstrating significant enhancements through a re-calibration protocol.

Contribution

The paper develops a general utility measurement framework for high-dimensional LDP mechanisms and proposes a re-calibration protocol that enhances their performance without altering existing schemes.

Findings

The framework benchmarks existing LDP mechanisms effectively.

Naive aggregation is sub-optimal in high-dimensional settings.

The HDR4ME protocol improves utility in high-dimensional mean estimation.

Abstract

Local differential privacy (LDP), which perturbs the data of each user locally and only sends the noisy version of her information to the aggregator, is a popular privacy-preserving data collection mechanism. In LDP, the data collector could obtain accurate statistics without access to original data, thus guaranteeing privacy. However, a primary drawback of LDP is its disappointing utility in high-dimensional space. Although various LDP schemes have been proposed to reduce perturbation, they share the same and naive aggregation mechanism at the side of the collector. In this paper, we first bring forward an analytical framework to generally measure the utilities of LDP mechanisms in high-dimensional space, which can benchmark existing and future LDP mechanisms without conducting any experiment. Based on this, the framework further reveals that the naive aggregation is sub-optimal in high-dimensional space, and there is much room for improvement. Motivated by this, we present a re-calibration protocol HDR4ME for high-dimensional mean estimation, which improves the utilities of existing LDP mechanisms without making any change to them. Both theoretical analysis and extensive experiments confirm the generality and effectiveness of our framework and protocol.