Consistent Estimation of Numerical Distributions under Local Differential Privacy by Wavelet Expansion
This addresses a domain-specific challenge in privacy-preserving data analysis for numerical data, offering incremental advances over prior work on categorical data.
The paper tackles the problem of estimating numerical distributions under local differential privacy (LDP), where existing methods for categorical data fail due to probability mass misplacement. The result is a wavelet expansion method that prioritizes low-order coefficients, achieving significant improvements over existing solutions in Wasserstein and KS distances.
Distribution estimation under local differential privacy (LDP) is a fundamental and challenging task. Significant progresses have been made on categorical data. However, due to different evaluation metrics, these methods do not work well when transferred to numerical data. In particular, we need to prevent the probability mass from being misplaced far away. In this paper, we propose a new approach that express the sample distribution using wavelet expansions. The coefficients of wavelet series are estimated under LDP. Our method prioritizes the estimation of low-order coefficients, in order to ensure accurate estimation at macroscopic level. Therefore, the probability mass is prevented from being misplaced too far away from its ground truth. We establish theoretical guarantees for our methods. Experiments show that our wavelet expansion method significantly outperforms existing solutions under Wasserstein and KS distances.