Reproduce “Learning interpretable continuous-time models of latent stochastic dynamical systems” on OpenResearch

About this paper

Lea Duncker, Gergo Bohner, Julien Boussard, Maneesh Sahani

The authors present a continuous-time latent stochastic model that learns trajectories and nonparametric dynamics from noisy, irregular observations. A Gaussian-process drift is conditioned on learned equilibrium points and Jacobians, while variational Bayes jointly infers paths and parameters. Simulations recover dynamics; in a double-well example, an extra fourth candidate becomes uncertain. Evidence is limited to simulated Gaussian and point-process observations.

Key insights

• Directly conditioning a nonparametric GP prior on interpretable dynamical features like fixed points and Jacobians enables simultaneous learning of complex system behavior and its mechanistic interpretation.
• A robust variational inference framework can effectively infer fully latent continuous-time SDEs and their dynamics from indirect, noisy, high-dimensional observations with irregular sampling and non-Gaussian likelihoods.
• The approach allows for automatic selection and pruning of fixed points through learned noise variance parameters, enhancing the accuracy and parsimony of the inferred dynamical portrait.

Summary by alphaXiv.