Variational Inference for Continuous-Time Switching Dynamical Systems
This work addresses the challenge of modeling and inference in continuous-time systems for applications such as biology and engineering, offering an incremental improvement over existing methods by combining Gaussian process approximations with Markov jump process inference.
The paper tackled the problem of inference in continuous-time switching dynamical systems, which are common in fields like biology, by developing a new variational inference algorithm that provides Bayesian latent state estimates and parameter point estimates, achieving computational tractability and demonstrating effectiveness in both simulated and real-world examples.
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on an Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.