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

2025-06-13

AI Summary

In high-stakes domains such as healthcare, individuals often contribute only single-time-point observations—not full temporal trajectories—posing a fundamental challenge for privacy-preserving synthetic trajectory generation. Method: We propose the first continuous-time synthetic trajectory generation framework supporting single-point inputs. Our approach establishes theoretical equivalence between mean-field Langevin dynamics and noisy particle gradient descent, integrating differential privacy noise injection, discrete particle system simulation, and marginal modeling via stochastic differential equations (SDEs). Contribution/Results: We achieve the first strictly (ε,δ)-differentially private continuous-time trajectory synthesis from single-time-point contributions—eliminating reliance on complete input trajectories. This substantially alleviates the privacy–utility trade-off. Experiments on a temporal variant of handwritten MNIST demonstrate that our generated trajectories exhibit high fidelity and superior utility compared to existing methods requiring full-trajectory inputs.

Technology Category

• Machine Learning: Privacy
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Privately generate continuous-time synthetic trajectory data
• Apply mean-field Langevin dynamics for time-series synthesis
• Ensure privacy for single-time-point contributions, not full trajectories

Innovation

• Private continuous-time data generation algorithm
• Mean-field Langevin dynamics for synthesis
• DP guarantees with single time-point contributions