Gaussian Variational Approximation for High-Dimensional State Space Models

• Activity Number: 400 - Recent Advances in Bayesian Computation and Modeling of High-Dimensional Multivariate Data
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Robert Kohn* and Matias Quiroz and David J Nott
• Companies: Univ of New South Wales and University of New South wales and National University of Singapore
• Keywords: Dynamic factor model; Gaussian variational approximation; stochastic gradient; Matrix Stochastic Volatility

Abstract

We consider variational approximations of the posterior distribution in a high-dimensional state space model. The variational approximation is a multivariate Gaussian. 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 parametrizations of the covariance structure when the number of model parameters is large. The joint posterior distribution over the high-dimensional state vectors is approximated using a dynamic factor model, with Markovian dependence in time 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 illustrate our approach in two high-dimensional applications which are challenging for MCMC sampling. The first is a spatio-temporal model for the spread of the Eurasian Collared-Dove across North America. The second is a multivariate stochastic volatility model for financial returns via a Wishart process.