Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamics
This work addresses privacy concerns in generating synthetic time-series data for sensitive applications, representing an incremental improvement over prior methods.
The paper tackles the problem of privately generating continuous-time synthetic trajectory data, which is crucial for sensitive domains like healthcare, by developing an algorithm based on mean-field Langevin dynamics. The method achieves realistic trajectory generation on hand-drawn MNIST data with meaningful privacy guarantees, while improving privacy characteristics by requiring each person to contribute data for only one time point instead of their entire temporal trajectory.
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.