Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamics

TL;DR

This paper introduces a novel differentially private algorithm for generating continuous-time synthetic trajectories, leveraging mean-field Langevin dynamics, with applications in sensitive domains like healthcare.

Contribution

It presents a new method that improves privacy by requiring each individual to contribute data at only one time point, unlike prior methods needing full trajectories.

Findings

Successfully generates realistic trajectories with privacy guarantees.

Achieves strong utility when each person contributes only one data point.

Outperforms prior methods in privacy-utility trade-offs.

Abstract

We provide an algorithm to privately generate continuous-time data (e.g. marginals from stochastic differential equations), which has applications in highly sensitive domains involving time-series data such as healthcare. We leverage the connections between trajectory inference and continuous-time synthetic data generation, along with a computational method based on mean-field Langevin dynamics. As discretized mean-field Langevin dynamics and noisy particle gradient descent are equivalent, DP results for noisy SGD can be applied to our setting. We provide experiments that generate realistic trajectories on a synthesized variation of hand-drawn MNIST data while maintaining meaningful privacy guarantees. Crucially, our method has strong utility guarantees under the setting where each person contributes data for \emph{only one time point}, while prior methods require each person to contribute their \emph{entire temporal trajectory}--directly improving the privacy characteristics by construction.