What are the applications of Multi-outputs Gaussian processes (MOGPs) in your work?

Hi everyone,

I am going to incorporate the Multi-output Gaussian processes (MOGPs) supports for PyMC GP v4 module. Mostly focus on Coregion regression and Hadamard kernel.

I would like to ask everyone in our community for your opinions if you are working or worked on Multi-output GPs, both in academics and business contexts:

  • What applications and/or problems are you apply the MOGPs for?
  • What libraries/packages do you use for MOGPs, and on what kinds of datasets?
  • What challenges do you face when implementing/applying MOGPs in your work?

Also, if you have any suggestions for implementing of MOGPs in PyMC v4, please let me know.

Many thanks!


I have been in meetings lately where colleagues are interested in jointly modelling the spatial variability of over one risk factor for cancer across a geographical map. The dataset has approximately 2000 spatial observations. CARBayes (an R package) supports "multivariate CAR " models. CAR models are sort of GPs, but the kernel is only non-zero if the two observations are spatial neighbours. This allows one to attempt either integrated nested Laplace approximations (INLA) or MCMC methods. In practice, I have found using any MCMC-style algorithm other than HMC means waiting forever to get any reasonable form of convergence.

Also have talked with people using gstats (another R package) for co-kriging, which is essentially the same as multi-output GPs (I think?). They were looking at modelling multiple mineral measurements at the same mining sites. Not too sure how they found it.



Hi @conorhassan

Thank you for sharing, it is interesting to know that MOGPs are applied in cancer research, and also in mining industry. I will check these R packages :slight_smile

Yes, Cokriging, which was come from Geostatistics, seems similar to a Linear Coregion Model. This lecture on multi-outputs GPs has mentioned about Cokriging.

Seem to me that many datasets in MOGPs have spatial/location characteristics.