The recent Predictive Linear Gaussian model (or PLG) improves upon traditional linear dynamical system models by using a predictive representation of state, which makes consistent parameter estimation possible without any loss of modeling power and while using fewer parameters. In this paper we extend the PLG to model stochastic, nonlinear dynamical systems by using kernel methods. With a Gaussian kernel, the model admits closed form solutions to the state update equations due to conjugacy

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... en the dynamics and the state representation. We also explore an efficient sigma-point approximation to the state updates, and show how all of the model parameters can be learned directly from data (and can be learned on-line with the Kernel Recursive Least-Squares algorithm). We empirically compare the model and its approximation to the original PLG and discuss their relative advantages.