How to check the kernel parameter values of a Gaussian process regression (GPR) model after training

I am trying to train a GPR model with the length scale of the kernel function in certain range. Therefore, I did the following ( follow this example ):

params = hyperparameters('fitrgp',X,y);
params(4).Range = [1,10];
gprMdl = fitrgp(X, y, 'OptimizeHyperparameters', params);

However, after training, I found that the kernel parameters in the trained model is empty. This confuses me a lot and I tried different ranges of kernel parameters and found that this restriction on its range actually worked. So I was wondering how I could obtain the exact value of kernel parameters from the trained GPR model. Thanks in advance!

Answer 1

[Don Mathis]

You can see the kernel parameters like this:

gprMdl.KernelInformation.KernelParameters

By default, params(4) (KernelScale) is not optimized. To optimize it, you'll need to set the Optimize field:

params = hyperparameters('fitrgp',X,y);
params(4).Range = [1,10];
params(4).Optimize = true;
gprMdl = fitrgp(X, y, 'OptimizeHyperparameters', params);
gprMdl.KernelInformation.KernelParameters

[Shoubo]

Thanks very much. One more thing I want to ask is how MATLAB determines the initial KernelScale by default?

[Don Mathis]

Check the "Algorithms" section of the fitrgp Doc page: https://www.mathworks.com/help/stats/fitrgp.html?searchHighlight=fitrgp&s_tid=doc_srchtitle#mw_303e137f-f50d-407f-8e66-10a741b0bef9

[Shoubo]

Thanks. I did read that but still felt confused. It says that the value of "KernelParameters" is a vector which contains the initial values of signal std and length scale but does not mention how those initial values are determined by default.

[Don Mathis]

That's described in the section on the KernelParameters argument: https://www.mathworks.com/help/stats/fitrgp.html?searchHighlight=fitrgp&s_tid=doc_srchtitle#input_argument_namevalue_d119e335756

[Shoubo]

Got it. Thank you so much for your time!