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Activity Number: 146 - Scaling up Bayesian Inference for Massive Data Sets
Type: Invited
Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #300362 Presentation
Title: Gaussian Variational Approximation for High-Dimensional State Space Models
Author(s): Robert Kohn*
Companies: University of New South Wales
Keywords: Dynamic factor; Gaussian variational approximation; stochastic gradient

We consider variational approximations of the posterior distribution in a high-dimensional state space model. The variational approximation is a multivariate Gaussian density, in which the variational parameters 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 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 Markov chain Monte Carlo sampling.

Authors who are presenting talks have a * after their name.

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