Expectation Propagation for Inference in Non-Linear Dynamical Models with Poisson Observations

Neural activity unfolding over time can be modeled using non-linear dynamical systems [1]. As neurons communicate via discrete action potentials, their activity can be characterized by the numbers of events occurring within short pre-defined time-bins (spike counts). Because the observed data are high-dimensional vectors of non-negative integers, non-linear state estimation from spike counts presents a unique set of challenges. In this paper, we describe why the expectation propagation (EP) framework is particularly well-suited to this problem. We then demonstrate ways to improve the robustness and accuracy of Gaussian quadrature-based EP. Compared to the unscented Kalman smoother, we find that EP-based state estimators provide more accurate state estimates.