Recursive Gaussian Process State Space Model

TL;DR

This paper introduces a recursive Gaussian Process State-Space Model (GPSSM) with adaptive online learning capabilities, enabling efficient, accurate, and flexible modeling of dynamical systems from streaming data.

Contribution

It presents a novel recursive GPSSM with adaptive domain and hyperparameter updates, using linearization and informative inducing point selection for online learning.

Findings

Outperforms existing online GPSSM methods in accuracy

Achieves higher computational efficiency

Demonstrates strong adaptability on synthetic and real data

Abstract

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models (GPSSMs) have recently gained significant attention due to their combination of flexibility and interpretability. However, for online learning, the field lacks an efficient method suitable for scenarios where prior information regarding data distribution and model function is limited. To address this issue, this paper proposes a recursive GPSSM method with adaptive capabilities for both operating domains and Gaussian process (GP) hyperparameters. Specifically, we first utilize first-order linearization to derive a Bayesian update equation for the joint distribution between the system state and the GP model, enabling closed-form and domain-independent learning. Second, an online selection algorithm for inducing points is developed based on informative criteria to achieve lightweight learning. Third, to support online hyperparameter optimization, we recover historical measurement information from the current filtering distribution. Comprehensive evaluations on both synthetic and real-world datasets demonstrate the superior accuracy, computational efficiency, and adaptability of our method compared to state-of-the-art online GPSSM techniques.