Continual Release Moment Estimation with Differential Privacy

We proposeJoint Moment Estimation(JME), a method for continually and privately estimating both the first and second moments of a data stream with reduced noise compared to naive approaches. JME supports thematrix mechanismand exploits a joint sensitivity analysis to identify a privacy regime in which the second-moment estimation incurs no additional privacy cost, thereby improving accuracy while maintaining privacy. We demonstrate JME’s effectiveness in two applications: estimating the running mean and covariance matrix for Gaussian density estimation and model training with DP-Adam.