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

Local differential privacy (LDP), which perturbs each user's data 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 users' 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 collector's side. 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.