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I would use a multi dimensional gaussian modell for regression. Rasmussen has a book with an algoritm, but it is only for one dimension output. Any idea to modify it?
First, I presume that you know about http://www.gaussianprocess.org/gpml/code/matlab/doc/regression.html#ard, and this is not what you want.
Second, I consequently presume that your problem involves several functions. In this case, for most purposes, you can just run your regression on each function separately; that is, unless you have some weird norm on the output space prescribed to you.