Novel approximations for inference in nonlinear dynamical systems using expectation propagation

We formulate the problem of inference in nonlinear dynamical systems in the framework of expectation propagation, and propose two novel algorithms. The first algorithm is based on Laplace approximation and allows for iterated forward and backward passes. The second is based on repeated application of the unscented transform. It leads to an unscented Kalman smoother for which the dynamics need not be inverted explicitly. In experiments with a one-dimensional nonlinear dynamical system we show that for relatively low observation noise levels, the Laplace algorithm allows for the best estimates of the state means. The unscented algorithm however is more robust to high observation noise and always outperforms the conventional inference methods against which it was benchmarked.