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I am trying to implement bayesian optimization using gauss process regression, and I want to try the multiple output GP firstly.

There are many softwares that implemented GP, like the fitrgp function in MATLAB and the ooDACE toolbox.

But I didn't find any available softwares that implementd the so called multiple output GP, that is, the Gauss Process Model that predict vector valued functions.

So, Are there any softwares that implemented the multiple output gauss process that I can use directly?

Alaya
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I am not sure my answer will help you as you seem to search matlab libraries.

However, you can do co-kriging in R with gstat. See http://www.css.cornell.edu/faculty/dgr2/teach/R/R_ck.pdf or https://github.com/cran/gstat/blob/master/demo/cokriging.R for more details about usage.

The lack of tools to do cokriging is partly due to the relative difficulty to use it. You need more assumptions than for simple kriging: in particular, modelling the dependence between in of the cokriged outputs via a cross-covariance function (https://stsda.kaust.edu.sa/Documents/2012.AGS.JASA.pdf). The covariance matrix is much bigger and you still need to make sure that it is positive definite, which can become quite hard depending on your covariance functions...

Pop
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    I know cokriging, there is a cokriging implementation in ooDACE toolbox, but I don't think that is what I want. To my understanding, for cokriging, there is only one "hidden black function", but you have multiple evaluators for that function, different evaluators have different accuracy and evluation cost, so you can use the relatively cheap evaluator to correct the accurate but expensive evluator. – Alaya Oct 08 '16 at 01:16
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    Yes, cokriging can be used for this so called "multi-fidelity" setting but also for predicting (tightly) correlated outputs. Then what do you want, if you do not want cokriging? – Pop Oct 10 '16 at 09:49
  • I am searching for some implementation of the so called "Multi Task Bayesian Optimization" mentioned in http://papers.nips.cc/paper/5086-multi-task-bayesian-optimization, and luckily I found one in https://github.com/ebonilla/mtgp, but I will also try co-kriging for comparison. – Alaya Oct 11 '16 at 06:25