Locally differentially private multi-dimensional data collection via haar transform

Abstract

Local differential privacy (LDP) has emerged as a privacy standard for collecting distributed data. In multi-dimensional data collection, separately perturbing each dimension is one canonical solution to protect privacy. Yet, it commonly falls short in statistical utility due to excessive noise injection caused by the privacy budget split linearly related to data dimensions. To tackle this problem, we propose a multi-dimensional data collection scheme under LDP, called PPMC, achieving privacy-utility tradeoff through Haar transform-based dimension reduction. Specifically, we apply Haar transform to convert multi-dimensional data into two parts: the average value and eigenvector, so as to lay a foundation for reducing the dimension. We design a probability density-based perturbation mechanism for the average value, which can decrease the noise injection by optimizing the probability distribution. For the eigenvector, a dimension reduction model is presented that promises low utility loss by error-balanced strategy. Further, we develop a global perturbation mechanism for the reduced dimension eigenvector, which can better maintain statistical utility while ensuring privacy via a private sampling strategy. Finally, the noisy multi-dimensional data is generated by utilizing the inverse Haar transform in a locally differential private manner. Theoretical analysis and experiment results confirm the effectiveness of our solution.