Variational Gaussian Process State-Space Models

TL;DR

This paper introduces a variational Bayesian method for learning nonlinear state-space models using sparse Gaussian processes, enabling efficient, flexible, and scalable inference for complex dynamical systems.

Contribution

It proposes a novel hybrid inference algorithm combining variational Bayes and sequential Monte Carlo for nonlinear state-space models with Gaussian processes.

Findings

Provides a tractable posterior over nonlinear dynamical systems.

Enables trade-off between model capacity and computational cost.

Supports stochastic variational inference and online learning for long time series.

Abstract

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.