Differentially private density estimation via Gaussian mixtures model

Density estimation can construct an estimate of the probability density function from the observed data. However, such a function may compromise the privacy of individuals. A notable paradigm for offering strong privacy guarantees in data analysis is differential privacy. In this paper, we propose DPGMM, a parametric density estimation algorithm using Gaussian mixtures model (GMM) under differential privacy. GMM is a well-known model that could approximate any distribution and can be solved via Expectation-Maximization (EM) algorithm. The main idea of DPGMM is to add two extra steps after getting the estimated parameters in the M step of each iteration. The first step is the noise adding step, which injects calibrated noise to the estimated parameters according to their L1-sensitivities and privacy budgets. The second step is the post-processing step, which post-processes those noisy parameters that might break their intrinsic characteristics. Extensive experiments using both real and synthetic datasets evaluate the performance of DPGMM, and demonstrate that the proposed method outperforms a state-of-art approach.