Gaussian variational approximation for high-dimensional state space models
arXiv:1801.07873
Abstract
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. 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. We approximate the joint posterior distribution over the high-dimensional state vectors by a dynamic factor model, having Markovian time dependence and a factor covariance structure for the states. This gives a reduced description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. The usefulness of the approach is illustrated for prediction in two high-dimensional applications that are challenging for Markov chain Monte Carlo sampling. The first is a spatio-temporal model for the spread of the Eurasian Collared-Dove across North America; the second is a Wishart-based multivariate stochastic volatility model for financial returns.
Significantly revised, especially the multivariate stochastic volatility model example
References in corpus (8)
- ADADELTA: An Adaptive Learning Rate Method
- The pseudo-marginal approach for efficient Monte Carlo computations
- Inferring Parameters and Structure of Latent Variable Models by Variational Bayes
- Frequentist Consistency of Variational Bayes
- Variational Bayesian Inference with Stochastic Search
- Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference
- Variational Boosting: Iteratively Refining Posterior Approximations
- Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era