Non-Gaussian Process Dynamical Models

Probabilistic dynamical models used in applications in tracking and prediction are typically assumed to be Gaussian noise driven motions since well-known inference algorithms can be applied to these models. However, in many real world examples deviations from Gaussianity are expected to appear, e.g., rapid changes in speed or direction, which cannot be reflected using processes with a smooth mean response. In this work, we introduce the non-Gaussian process (NGP) dynamical model which allow for straightforward modelling of heavy-tailed, non-Gaussian behaviours while retaining a tractable conditional Gaussian process (GP) structure through an infinite mixture of non-homogeneous GPs representation. We present two novel inference methodologies for these new models based on the conditionally Gaussian formulation of NGPs which are suitable for both MCMC and marginalised particle filtering algorithms. The results are demonstrated on synthetically generated data sets.