Continual Release Moment Estimation with Differential Privacy

Nikita Kalinin, Jalaj Upadhyay, Christoph H. Lampert

Advances in Neural Information Processing Systems 38 Main Conference (NeurIPS 2025) Main Conference Track DOI: 10.52202/085713-1924

We propose Joint 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 the matrix mechanism and 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.