  The Gaussian process state-space model (GPSSM) has attracted extensive
attention for modeling complex nonlinear dynamical systems. However, the
existing GPSSM employs separate Gaussian processes (GPs) for each latent state
dimension, leading to escalating computational complexity and parameter
proliferation, thus posing challenges for modeling dynamical systems with
high-dimensional latent states. To surmount this obstacle, we propose to
integrate the efficient transformed Gaussian process (ETGP) into the GPSSM,
which involves pushing a shared GP through multiple normalizing flows to
efficiently model the transition function in high-dimensional latent state
space. Additionally, we develop a corresponding variational inference algorithm
that surpasses existing methods in terms of parameter count and computational
complexity. Experimental results on diverse synthetic and real-world datasets
corroborate the efficiency of the proposed method, while also demonstrating its
ability to achieve similar inference performance compared to existing methods.
Code is available at \url{https://github.com/zhidilin/gpssmProj}.
