Approximate Inference in Latent Diffusion Processes from Continuous Time Observations

We propose a novel approximate inference approach for continuous time stochastic dynamical systems observed in both discrete and continuous time with noise. Our expectation-propagation approach generalises the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models with point process observations) and box likelihood models. Experimental results on real and simulated data demonstrate high distributional accuracy and significant computational savings compared to discrete-time approaches in a neural application.