  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.
