Streaming Variational Monte Carlo

TL;DR

This paper introduces an online Bayesian inference framework combining variational inference and sequential Monte Carlo for nonlinear state-space models, enabling real-time, accurate filtering with interpretable latent dynamics.

Contribution

The paper presents a novel online learning method that efficiently approximates the filtering posterior in nonlinear state-space models using sparse Gaussian processes.

Findings

Provides arbitrarily close approximation to true filtering distribution

Achieves constant time complexity per sample

Enables real-time online learning with interpretable models

Abstract

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.