Dear UQLab developers,
For a project I’m working on, I need to define a Gaussian process with a custom-defined correlation function and unitary process variance. The reason is that the covariance/kernel function cannot be expressed as k(x,x’) = sigma^2*r(x,x’), therefore I would like to set sigma^2 = 1 to be able to play with r(x,x’) only.
However, in my understanding, it is possible to fix the value of SigmaSQ only when working with a known noise variance. For example, the code below would do for a user-defined Gaussian correlation function with unitary variance:
MetaOpts.Corr.Family = @(x1,x2,theta) exp(-1/2 * (x1-x2).^2/theta^2);
MetaOpts.Corr.Type = 'separable';
MetaOpts.Regression.SigmaNSQ = 1e-6;
MetaOpts.Regression.SigmaSQ.InitialValue = 1;
MetaOpts.Regression.SigmaSQ.Bound = [1,1]';
However, this would force the noise variance to 1e-3. While this might still be OK, I was wondering whether there exist some workaround to be able to work with
MetaOpts.Regression.SigmaNSQ = 'auto';
Please note that I was able to implement a custom solution myself. However, I was wondering if there is a way to rely on the UQLab toolbox given the pletora of hyperparameter optimization options it offers.
Finally, I take the opportunity to point out that the abovementioned options for the process variance are erroneousy indicated to be in MetaOpts.Optim.Regression.SigmaSQ (instead of MetaOpts.Regression.SigmaSQ) in the caption of Table 17 of the User Manual.