Problem training Gaussian process with 'ardsquaredexponential' kernel function using bayesopt

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Robert on 24 Mar 2022
Commented: Alan Weiss on 28 Apr 2022
Dear community,
I have a problem training a Gaussian process using fitrgp. Can someone advise, why some datasets will produce errors when training with the command below. The training data set that is causing the error is in the attached mat-file.
gpr = fitrgp(X, y, ...
'KernelFunction', 'ardsquaredexponential',...
'PredictMethod', 'fic',...
'OptimizeHyperparameters', {'KernelScale','Sigma'},...
'Optimizer', 'bayesopt',...
'Repartition', false,...
'UseParallel', true,...
'Kfold' , 5),...
'Verbose', 1,...
'OptimizerOptions', statset(...
'Display', 'final',...
'UseParallel', true));
The error that is returned reads
For the 'ARDSquaredExponential' kernel with 2 predictors, 'KernelParameters' must be a 3-by-1 vector of positive numbers.
and did not help me find a solution. (I already tried normalizing, more data, etc., but it did not work)
Best regards and thank you,

Accepted Answer

Alan Weiss
Alan Weiss on 24 Mar 2022
As stated in the documentation for OptimizeHyperparameters:
"KernelScale cannot be optimized for any of the ARD kernels."
Alan Weiss
MATLAB mathematical toolbox documentation
Alan Weiss
Alan Weiss on 28 Apr 2022
I don't think so, but you can try setting the name (not function handle) of your user-defined kernel function as the kernel by using hyperparameters to set a nondefault kernel, as outlined on the fitrgp reference page in the HyperparameterOptimizationOptions section. I haven't tried this and don't know if it will work--I suspect not, but it might be worth a try.
Alan Weiss
MATLAB mathematical toolbox documentation

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