Streaming Variational Monte Carlo
This enables flexible and accurate Bayesian joint filtering for real-time applications in complex dynamical systems.
The paper tackles the challenge of simultaneous inference of state and nonlinear dynamics in streaming time series data, achieving an approximation of the filtering posterior that can be made arbitrarily close to the true distribution with constant time complexity per sample.
Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications.