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How does bayesian optimization and cross-validation work?

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Dimitri
Dimitri on 23 Aug 2019
Commented: Don Mathis on 23 Aug 2019
Hello,
I was wondering how exactly the hyperparameter optimization works in this example: Example. The default setting is 5-fold cross-validation, but the output is a normal RegressionSVM and not a RegressionPartitionedSVM. That's how I understand the process, please give me feedback.
Let´s consider the first step of the hyperparameter optimization. The algorithm choses a initial hyperparameter setting and learns a model with 4/5 of the data. Now it evaluates the performance on the 1/5 of the data. What happens next? Is this hyperparameter setting used again and one model learned on another of the 4/5 data? After 5 iterations you now have 5 objectiv function values which are used for the calculation of the loss? This loss is the final loss for the first hyperparameter setting. This procedure is now repeated 30 times?

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Accepted Answer

Don Mathis
Don Mathis on 23 Aug 2019
Edited: Don Mathis on 23 Aug 2019
In each iteration of the optimization, fitrsvm is called with 5-fold crossvalidation, using a particular vector of hyperparameters. This results in a RegressionPartitionedSVM. Then the kfoldLoss method is called on that object, obtaining the Loss for that vector of hyperparameters. That Loss value is printed in the command line display in the "Objective" column for that iteration.
In the next iteration, a new vector of hyperparameters is chosen, and the process is repeated.
Finally, after 30 (by default) iterations, the "best" hyperparameter vector is chosen, and a final model is trained on the entire dataset using those hyperparameters, without crossvalidation. That final RegressionSVM model is returned.

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Don Mathis
Don Mathis on 23 Aug 2019
To be precise, the Objective value is log(1+Loss) for regression models.

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