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When doing maching learning tasks, it is common to divide the whold data set into three unoverlapping subsets, namely training set, validation set and test set. I understand that the test set should be excluded during the model developmet process and scaling is usually needed in the data pre-processing stage. However, I'm not sure which data sets should I use to calculate the scalers. Should I use scalers calculated from the training set or scalers calculated from both the training set and the validation set?

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You should use scalers fitted on the training set, and use it on validation and test sets. But, if you refit using train+validation after your validation loops (e.g. for HPO), you should use scalers fitted on train+validation and use it on the test set.

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