Output-Dependent Gaussian Process State-Space Model
This work addresses a specific modeling issue in probabilistic state-space models for researchers in machine learning, representing an incremental improvement by incorporating output dependencies.
The paper tackled the limitation of existing Gaussian process state-space models (GPSSMs) by introducing an output-dependent version using the linear model of coregionalization (LMC) framework to capture dependencies between outputs, resulting in improved learning and inference performance on synthetic and real datasets.
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.