How to model noise-free case and to obtain Covarince matrix after performing Gaussian process regression using fitrgp

Assume that there is a GP model constructed using D = {X, y} with fitrgp function, such that:

gprMdl = fitrgp(data.X, data.Y, 'KernelFunction', 'ardsquaredexponential', 'BasisFunction', 'none', 'verbose', 1, 'FitMethod',exact')

I have several question as follows:

1) In introduction of GPR, it says GPR can be used to model the noise and noise-free cases (two present figures in Gaussian Process Regression Models page of MATLAB). But I didn't find how to model noise-free (deterministic) case with fitrgp function.

2) How can I get the auxiliary terms (such as covarince matrix C=K(X,X), and its inverse) that are already used when training GPR? I know we can calculate them by ourselves, but if matlab can produce them or not according to users' selection, it may be better.I need these auxiliary terms to do things else.

HP

[kele xu]

I have the same question, how to model noise-free case with fitrgp function.

[Shenglin Huang]

Same question. This problem is really confusing.

Answer 1

[Gautam Pendse]

You can set 'Sigma' to a small value and set a name value pair called ConstantSigma to true. That way the initial value specified in 'Sigma' will not be optimized.

Hope this helps,

Gautam

[Pengfei Wei]

Thanks for you answer. I have made the set ('Sigma',0.0001,'ConstantSigma',true) for my test, but the sigma value in the trained GPR model turn out to be 0.0120. Since I also want to use the GPR model in a interpolation way, I am quite strugglling with this issue. Besides, can I get the covariance matrix of the training data directly from the trained model? Thank you!

[Sterling Baird]

For the sigma value, maybe try changing 'SigmaLowerBound' to a lower value (defaults to 1e-2*std(y)). If you figure this out, I'd be interested to know as well. Where are you checking to get 0.0120?

For the covariance matrix: https://www.mathworks.com/matlabcentral/answers/251782-calculating-the-matrix-k-at-test-inputs-after-training-a-gaussian-process-with-fitrgp#answer_199144