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I have a set of SVM models that I am trying to compare. Each of the models is trained on a variation of the original data:

  • The original data
  • The original data using resampling scheme A
  • The original data using resampling scheme B

When I train the models, I use grid search to estimate the SVM hyperparameter $C$ and I get different values under each scheme.

The overall hypothesis that I am trying to test is whether or not resampling scheme B yields a model that performs better than resampling method A.

Is simply comparing performance metrics between scheme B and A acceptable? Or should I be using the same hyperparameters for the models for both schemes?

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Indeed resampling methods can affect the performance of a model. This is particularly true when the data is imbalanced.

There is no reason to think the $C$ that you chose should be "universal" and I am not surprised that the best $C$ parameter depends on the sampling scheme you use to fit the model.

I assume that you used cross validation to evaluate the performance of each scheme, so you have to be very careful with the standard deviation of the performances obtained.

A last point to stress is the fact that, the more models you test, the more likely you are to find a model whose performance surpasses all the other models, out of pure luck.

With all this in mind, I would feel comfortable using a grid ($C$, sampling scheme) that does not contains too many elements.

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