Hi Quaglino,

You are right that at predict time both are not equivalent.

More specifically, in Eq 2.23 in http://www.gaussianprocess.org/gpml/chapters/RW2.pdf

1. If you use a WhiteKernel, the first term becomes K^{hat}(X*, X) + \sigma^2 where K^{hat} is the kernel that you are using apart from the WhiteKernel and \sigma^2 is 
the noise term learnt by the WhiteKernel.

2. If you set noise to be alpha, the first term is just  K^{hat}(X*, X)

Thanks!


On Fri, Apr 7, 2017 at 4:06 AM, Quaglino Alessio <alessio.quaglino@usi.ch> wrote:
Hello,

I am trying to understand if alpha is truly equivalent to WhiteKernel by looking at gpr.py. 

I can see that that the two are the same when fit() is called, i.e. self.L_ and self.alpha_ are the same whether alpha or WhiteKernel is used. 

In predict(), however, y_var = self.kernel_.diag(X) produces a different result depending on whether alpha or WhiteKernel is used. Is this correct? Indeed, if I run http://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_noisy.html the grey areas are completely different depending on which one I use, although the red and black curves are exactly the same.

Thank you in advance!

Regards,
-------------------------------------------------
Dr. Alessio Quaglino
Postdoctoral Researcher
Institute of Computational Science
Università della Svizzera Italiana


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