LDPTube: Theoretical Utility Benchmark and Enhancement for LDP Mechanisms in High-Dimensional Space

While collecting data from a large population, local differential privacy (LDP), which only sends users’ perturbed data to the data collector, becomes a popular solution to preserving each user's privacy. However, as high-dimensional data collection becomes prevalent for machine learning, LDP suffers from low utility (a.k.a., the dimensionality curse) as its privacy budget in each dimension is severely diluted. In a previous work (Duan et al. 2022), we proposed an analytical framework for benchmarking various LDP mechanisms and a re-calibration protocol for its utility enhancement in high-dimensional space. However, they have several limitations, including difficulty in setting a suitable benchmark parameter (i.e., the probabilistic supremum of deviation), a mismatch of the metric with prevalent experimental metrics, and costly re-benchmarking operation upon population change. In this paper, we propose a toolbox LDPTube to address these issues. It first consists of a non-parametric benchmark in high-dimensional space, which adopts MSE as the metric and avoids re-benchmarking upon population change. Then we adapt this benchmark to personalized LDP, where each user can choose her own privacy budget and privacy region. Last but not the least, we enhance the re-calibration protocol in (Duan et al. 2022) by an adaptive protocol HDR4ME* that opportunistically chooses suitable regularization terms that can maximize utility. We verify the correctness and effectiveness of these new solutions by both theoretical analysis and experimental results.