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How bayesopt find kernel parameters

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Aep
Aep on 4 Sep 2020
Commented: Aep on 2 Oct 2020
Hello all,
I know that bayesopt uses fitrgp to create gaussian process in each iteration. But how bayesopt find the optimize kernel parameters of the Gaussian process regression in each step? Does it optimize kernel parameters at all? If not, what are the kernel paramters being used in each iteration?
I want to know the default configurations of bayesopt for the items above, I was not able to find my answer in the documentation.
Thank you in advance

  1 Comment

Aep
Aep on 5 Sep 2020
Any help on this is greatly appreciated.

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Answers (1)

Mohith Kulkarni
Mohith Kulkarni on 25 Sep 2020
Edited: Mohith Kulkarni on 25 Sep 2020
By default the optimize parameter is set to 0 for the fitrgp KernelFunction and KernelScale hyperparmeters. Refer to the below code to change the parameter:
params = hyperparameters('fitrgp',X,y);
params(3).Optimize = true; %set KernelFunction optimize to true
params(4).Optimize = true; %set KernelScale optimize to true
In case of "fitrgp" fit function, check Hyperparameter Optimization section of fitrgp arguments for more information. You can check the default Kernel Function and Kernel Parameters of fitrgp fit function here:
you can then use the fit function in the objective function.
For more information on performing Bayesian Optimization using bayesopt refer to:

  3 Comments

Aep
Aep on 28 Sep 2020
Thank you for your explanations Mohith. As mentioned here , MATLAB uses matern 5/2 kernel function for bayesopt. So my main question is how the kernela paraemeters are found for this Kernel function in Bayesopt. As you mentioned the initial values of kernel parameters for matern 5/2 is mentioned here. So does the bayesopt uses these default values? If yes, how does these "initial" kernel parameters change in each iteration of bayesopt? or do they change at all or they remain the same in each iteration?
In other words: are the hyperparameters found by maximizing their marginal likelihood in the default configurations of bayesopt?
Mohith Kulkarni
Mohith Kulkarni on 30 Sep 2020
Regarding the second question, yes it does change. In each iteration, fitrgp is called with the default initial values for its own hyperparameters (covariance and the kernel parameters), and it's fitted from scratch every iteration. To avoid getting stuck with potentially poor parameters, BayesOpt does not start from the fitted values from the previous iteration.
Aep
Aep on 2 Oct 2020
Thank you very much for your answer Mohith. So as you mentioned the inital values are different in each iteration. But considering just one single iteration. We have some initial values. What happens to these values in that specific iteration in bayesopt? Do they change in that iteration? If yes, how?
I apologize if it is a basic question in Gaussian process. I am new to this and I want to make it clear for myself about how Bayesopt does this.

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