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

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'},...

'HyperparameterOptimizationOptions',...

struct('MaxObjectiveEvaluations',250,...

'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,

Robert

Answer 1

[Alan Weiss]

As stated in the documentation for OptimizeHyperparameters:

"KernelScale cannot be optimized for any of the ARD kernels."

Alan Weiss

MATLAB mathematical toolbox documentation

[Robert]

Thanks!

[Robert]

Does OptimizeHyperparameters support user-defined Kernels?

[Alan Weiss]

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

[Rebecca Mazloum]

Hello,

How are the KernelScales chosen for ARD kernnels?

We notice that initial values given as KernelParameters change once the model is created.

Are the KernelScales optimized internally for ARD kernels? And if so using which method?

Thanks