MATLAB: Problem with function handle for Basis function in fitrgp

Question

I like to use a custom Basis function for fitrgp.

beta0 = [1.5,2.0];
hfcn = @(X) (beta0(1).*(X).^beta0(2)); 

This should be a powerMean-function.

If I call:

gprMdl1 = fitrgp(x,y,'BasisFunction',hfcn,'Beta',beta0) 

with dummy-data from:

load(fullfile(matlabroot,'examples','stats','gprdata2.mat'))

I get

gprMdl1.Beta = 0.0019

Why is gprMdl1.Beta not 1×2 like beta0? Is it posible to optimize custom parameters in Basis function (like beta0)?

Answer 1

load(fullfile(matlabroot,'examples','stats','gprdata2.mat'))

In this case, your x is n x 1;

hfcn returns H, which has size n x 1; i.e. p = 1;

So if you want to provide 'Beta' to fitrgp(), it should be of size p x 1, i.e 1 x 1.

https://www.mathworks.com/help/stats/fitrgp.html#d117e376477

fitrgp() is only using your beta0(1) as Adam mentioned in the comment.