fitrgp hyperparameter optimization for noisy functions

hyperparameter optimization for fitrgp hyperparameters in matlab there is {'BasisFunction','KernelFunction','KernelScale','Sigma','Standardize'} that can be optimized. However, in noisy cases we have a sigma parameter (different than kernel sigma) added to the diagonal of the kernel based on Rasmussen, 2006. How can I specify or optimize that sigma besides sigmaf and sigmal which are the kernel hyperparameters?

Answer 1

[Aditya Patil]

From my understanding, you want to set the noise variance() parameter mentioned in the book. You can do so using 'Sigma' name value pair. Note that 'Sigma' sets the standard deviation. You can find more about it in the documentation here

Answer 2

[Hyunjung Lee]

The nugget or jitter can be "addressed" by adding a small number to the main diagonal of the correlation matrix.

I agree with Aditya Patil. In fitrgp, that can be done via 'Sigma'. For example,

tau=1e-3; %some small value
gpmodel=fitrgp(X,y,'FitMethod','none','Sigma',tau);

By setting 'FitMethod' to 'none', the nugget term remains as the value you assign.