Multi dimensonal output GPML?

Question

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?

Answer 1

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.

Answer 2

Lets say you want to model f(x,y) = [u , v]^T. You could model u and v separately:

f1(x,y) = u

f2(x,y) = v

This is making the assumption that u and v are conditionally independent given x, y. However, GPML advises that u and v can remain correlated because of a correlating noise process. Consult Chapter 9 of GPML for approaches in this case.