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Should data transformation techniques (ex: creating new features/ log attributes) be done before or after feature selection techniques (ex: mutual information feature selection)? Are there any implications if data transformation is performed first or vice versa?

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It makes sense to apply feature selection only after all the features have been created, otherwise the newly created/added features don't go through the feature selection stage. This might result in a model with a suboptimal set of features.

Of course, when one wants to apply the selection only on a subset of features then it makes sense to add the other features separately.

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