Differentially private density estimation with skew-normal mixtures model

The protection of private data is a hot research issue in the era of big data. Differential privacy is a strong privacy guarantees in data analysis. In this paper, we propose DP-MSNM, a parametric density estimation algorithm using Multivariate Skew-Normal Mixtures (MSNM) model to differential privacy. MSNM can solve the asymmetric problem of datasets, and it is could approximate any distribution through Expectation-Maximization (EM) algorithm. In this model,we add two extra steps on the estimated parameters in the M step of each iteration. The first step is adding calibrated noise to the estimated parameters based on Laplacian mechanism. The second step is post-processes those noisy parameters to ensure their intrinsic characteristics based on the theory of vector normalize and positive semi definition matrix. Extensive experiments using both real datasets evaluate the performance of DP-MSNM, and demonstrate that the proposed method outperforms DP-GMM.