DP-EM: Differentially Private Expectation Maximization
This addresses privacy-preserving estimation for iterative algorithms, with incremental improvements in noise reduction for applications like mixture models.
The paper tackles the challenge of making the iterative expectation maximization (EM) algorithm differentially private by proposing DP-EM, which uses moment perturbation and advanced composition methods to reduce noise; empirical results show benefits and similar performance for Gaussian mixture models.
The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently developed composition methods to bound the privacy "cost" of multiple EM iterations: the moments accountant (MA) and zero-mean concentrated differential privacy (zCDP). Both MA and zCDP bound the moment generating function of the privacy loss random variable and achieve a refined tail bound, which effectively decrease the amount of additive noise. We present empirical results showing the benefits of our approach, as well as similar performance between these two composition methods in the DP-EM setting for Gaussian mixture models. Our approach can be readily extended to many iterative learning algorithms, opening up various exciting future directions.