Generalised Wishart Processes

Andrew Gordon Wilson, Zoubin Ghahramani
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:809-822, 2011.

Abstract

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-wilson11a, title = {Generalised Wishart Processes}, author = {Wilson, Andrew Gordon and Ghahramani, Zoubin}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {809--822}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/wilson11a/wilson11a.pdf}, url = {https://proceedings.mlr.press/r9/wilson11a.html}, abstract = {We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Generalised Wishart Processes %A Andrew Gordon Wilson %A Zoubin Ghahramani %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-wilson11a %I PMLR %P 809--822 %U https://proceedings.mlr.press/r9/wilson11a.html %V R9 %X We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations. %Z Reissued by PMLR on 04 October 2026.
APA
Wilson, A.G. & Ghahramani, Z.. (2011). Generalised Wishart Processes. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:809-822 Available from https://proceedings.mlr.press/r9/wilson11a.html. Reissued by PMLR on 04 October 2026.

Related Material