# Gaussian variational approximation for high-dimensional state space models

arXiv: https://arxiv.org/abs/1801.07873 · HTML: https://mlsanity.com/paper/1801.07873/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2018.

## Built on by (most cited first, 10 of 10)

- [Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Space](https://mlsanity.com/paper/2304.05398/) (2023)
- [Sampling via Gradient Flows in the Space of Probability Measures](https://mlsanity.com/paper/2310.03597/) (2023)
- [Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance](https://mlsanity.com/paper/2302.11024/) (2023)
- [Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent](https://mlsanity.com/paper/2305.14076/) (2023)
- [Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows](https://mlsanity.com/paper/2406.17263/) (2024)
- [Federated Variational Inference Methods for Structured Latent Variable Models](https://mlsanity.com/paper/2302.03314/) (2023)
- [Accelerate Langevin Sampling with Birth-Death Process and Exploration Component](https://mlsanity.com/paper/2305.05529/) (2023)
- [Provably Scalable Black-Box Variational Inference with Structured Variational Families](https://mlsanity.com/paper/2401.10989/) (2024)
- [Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold](https://mlsanity.com/paper/2410.02490/) (2024)
- [Vector Copula Variational Inference and Dependent Block Posterior Approximations](https://mlsanity.com/paper/2503.01072/) (2025)

## Abstract (arXiv)

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.