Problem with function handle for Basis function in fitrgp

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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:
I get
gprMdl1.Beta = 0.0019
Why is gprMdl1.Beta not 1x2 like beta0? Is it posible to optimize custom parameters in Basis function (like beta0)?
Adam Danz
Adam Danz on 28 Jan 2020
"Why is gprMdl1.Beta not 1x2 like beta0?"
That basis function will return as many values as provided in the input X. X is multiplied by 1 value (beta0(1)) and added to one value (beta0(2)). So if X is only 1 value, the output should only be one value. If x is 1x5, the output will be 1x5; if x is 3x4, so is the output.
Adam Danz
Adam Danz on 21 Nov 2020
>gprMdl1.Beta is not 3x1, there is still only one beta. Could you help me check this?
Check this out.....
% Your function
beta0 = [1;2;3];
hfcn = @(X) ([ones(size(X,1),1),X,X.^2]*beta0);
% Test some inputs-outputs
ans = 6
ans = 3×1
6 17 34

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Accepted Answer

Ridwan Alam
Ridwan Alam on 28 Jan 2020
Edited: Ridwan Alam on 28 Jan 2020
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.
fitrgp() is only using your beta0(1) as Adam mentioned in the comment.
Stefan Hövel
Stefan Hövel on 28 Jan 2020
Okay, now I get it. Beta can be interpreted as a weight on the Basis function H. I would like fitrgp to find the optimal values for beta0 within hfcn. For the KernelFunction it is posible see Example: Fit GPR Model Using Custom Kernel Function:
kfcn = @(XN,XM,theta) (exp(theta(2))^2)*exp(-(pdist2(XN,XM).^2)/(2*exp(theta(1))^2));
Here fitrgp optimizes the theta-values (see KernelInformation). I suppose it is not posible for Basis function.
Thanks a lot!

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