[scikit-learn] Alpha in GaussianProcessRegressor

[Manoj Kumar]

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 at 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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>


-- 
Manoj,
http://github.com/MechCoder
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