Title: Gaussian variational approximations for high-dimensional state space models
Authors: Matias Quiroz - University of Technology Sydney (Australia) [presenting]
David Nott - National University of Singapore (Singapore)
Robert Kohn - University of New South Wales (Australia)
Abstract: Variational approximations of the posterior distribution in high-dimensional state space models, which encompass spatio-temporal models, are considered. The variational approximation is a multivariate Gaussian density, in which the variational parameters to be optimized are a mean vector and a covariance matrix. The number of parameters in the covariance matrix grows as the square of the number of model parameters, so it is necessary to find simple yet effective parameterizations of the covariance structure when the number of model parameters is large. The joint posterior distribution over the high-dimensional state vectors is approximated by a dynamic factor model, with Markovian time dependence and a factor covariance structure for the states. This gives a reduced dimension description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. We consider an application that models the spread of the Eurasian Collared-Dove across North America.