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 https://github.com/zhidilin/gpssmProj.

高斯过程状态空间模型（GPSSM）中引入了高效变换的高斯过程（ETGP）以及归一化流来有效地建模高维潜在状态空间中的转换函数，从而提高了模型的计算效率。此外，我们还开发了相应的变分推断算法，通过数量和计算复杂性的比较，优于现有方法。实验结果验证了该方法的效率，并证明其与现有方法相比具有相似的推断性能。