  In this paper, we propose a nonlinear probabilistic generative model of
Koopman mode decomposition based on an unsupervised Gaussian process. Existing
data-driven methods for Koopman mode decomposition have focused on estimating
the quantities specified by Koopman mode decomposition, namely, eigenvalues,
eigenfunctions, and modes. Our model enables the simultaneous estimation of
these quantities and latent variables governed by an unknown dynamical system.
Furthermore, we introduce an efficient strategy to estimate the parameters of
our model by low-rank approximations of covariance matrices. Applying the
proposed model to both synthetic data and a real-world epidemiological dataset,
we show that various analyses are available using the estimated parameters.
