We propose Joint Moment Estimation (JME), a method for continually and privately estimating both the first and second moments of data with reduced noise compared to naive approaches. JME uses the matrix mechanism and a joint sensitivity analysis to allow the second moment estimation with 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 on CIFAR-10.
@article{arxiv.2502.06597,
title = {Continual Release Moment Estimation with Differential Privacy},
author = {Nikita P. Kalinin and Jalaj Upadhyay and Christoph H. Lampert},
journal= {arXiv preprint arXiv:2502.06597},
year = {2025}
}