A latent manifold markovian dynamics gaussian process

Abstract

In this paper, we propose a Gaussian process model for analysis of nonlinear time series. Formulation of our model is based on the consideration that the observed data are functions of latent variables, with the associated mapping between observations and latent representations modeled through Gaussian process priors. In addition, to capture the temporal dynamics in the modeled data, we assume that subsequent latent representations depend on each other on the basis of a hidden Markov prior imposed over them. Derivation of our model is performed by marginalizing out the model parameters in closed form by using Gaussian process priors for observation mappings, and appropriate stick-breaking priors for the latent variable (Markovian) dynamics. This way, we eventually obtain a nonparametric Bayesian model for dynamical systems that accounts for uncertainty in the modeled data.We provide efficient inference algorithms for our model on the basis of a truncated variational Bayesian approximation. We demonstrate the efficacy of our approach considering a number of applications dealing with real-world data, and compare it to related state-of-the-art approaches.