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

• URL: http://arxiv.org/abs/2506.12203v1
• Date: Fri, 13 Jun 2025 20:13:37 GMT
• Title: Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamics
• Authors: Anming Gu, Edward Chien, Kristjan Greenewald,
• Abstract summary: We leverage the connections between trajectory inference and continuous-time synthetic data generation.<n>We provide experiments that generate realistic trajectories on a synthesized variation of hand-drawn MNIST data.
• Score: 2.7255073299359154
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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