Output-Dependent Gaussian Process State-Space Model

TL;DR

This paper introduces an output-dependent Gaussian process state-space model that leverages the linear model of coregionalization to better capture output dependencies, improving learning and inference performance.

Contribution

It proposes a novel output-dependent GPSSM using the LMC framework and a variational sparse GP method for efficient joint learning and inference.

Findings

Outperforms existing GPSSMs in synthetic data experiments

Demonstrates improved inference accuracy on real datasets

Maintains computational efficiency with minimal complexity increase

Abstract

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be independent, meaning that the GPSSMs cannot exploit the inductive biases between different outputs and lose certain model capacities. To address this issue, this paper proposes an output-dependent and more realistic GPSSM by utilizing the well-known, simple yet practical linear model of coregionalization (LMC) framework to represent the output dependency. To jointly learn the output-dependent GPSSM and infer the latent states, we propose a variational sparse GP-based learning method that only gently increases the computational complexity. Experiments on both synthetic and real datasets demonstrate the superiority of the output-dependent GPSSM in terms of learning and inference performance.