Gaussian process method improves learning from irregular noisy data
Simulation-Free Learning of GP-SDEs from Irregular Observations
Machine Learning
Summary
Understanding how complex systems change over time can be hard, especially when the data collected is noisy or happens at random times. The authors created a method that learns about such systems without time-consuming computer simulations. Their approach better captures the underlying patterns and uncertainty even when observations are irregular. Tests showed it works well on difficult systems and predicts future behavior more reliably than some existing approaches.
What this means in practice
- •For data scientists: Estimate continuous-time system dynamics accurately from sparse, noisy, and irregular time series data without costly simulations.
- •For control system engineers: Improve state estimation and forecasting of dynamic systems observed at irregular times for better system identification and control.
Authors
Zhidi Lin, Yuhao Liu, Ying Li, Edwin Fong, Petar Djurić
Abstract
Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz--63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.