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Poster
Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processes
Creighton Heaukulani · Mark van der Wilk

Tue Dec 10 05:30 PM -- 07:30 PM (PST) @ East Exhibition Hall B + C #150
in Probabilistic Methods -- Gaussian Processes »

We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, existing variational inference algorithms for which form the basis of our approach. These methods are easy to implement as a black-box and scale favorably with the length of the time series, however, they fail in the case of the Wishart process, an issue we resolve with a simple modification into an additive white noise parameterization of the model. This modification is also key to implementing a factored variant of the construction, allowing inference to additionally scale to high-dimensional covariance matrices. Through experimentation, we demonstrate that some (but not all) model variants outperform multivariate GARCH when forecasting the covariances of returns on financial instruments.

Keywords: Gaussian Processes · Probabilistic Methods · Applications -> Time Series Analysis; Probabilistic Methods; Probabilistic Methods · Bayesian Nonparametrics; Probabilistic Me
[ Paper]  [ Poster] 

Author Information

Creighton Heaukulani (Ministry of Health, Singapore)
Mark van der Wilk (PROWLER.io)

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