Mixtures of Predictive Linear Gaussian Models for Nonlinear, Stochastic Dynamical Systems

Abstract

The Predictive Linear Gaussian model (or PLG) im-proves upon traditional linear dynamical system mod-els by using a predictive representation of state, which makes consistent parameter estimation possible without any loss of modeling power and while using fewer pa-rameters. This work extends the PLG to model non-linear dynamical systems through the use of a kernel-ized, nonlinear mixture technique. The resulting gener-ative model has been named the “MPLG, ” for “Mix-ture of PLGs. ” We also develop a novel technique to perform inference in the model, which consists of a hybrid of sigma-point approximations and analytical statistics. We show that the technique leads to fast and accurate approximations, and that it is general enough to be applied in other contexts. We empirically explore the MPLG and demonstrate its viability on several real-world and synthetic tasks.