Hello,
It is preferable that you normalize data with respect to the parameters of training data only. You can of course normalize over the whole dataset but as you mentioned, that would introduce bias in the training process.
We want our test set to be as representative as possible of real data. We therefore don't want to use any information from the test set (including mean and variance) in the training process.
I hope that it answers your question.
Best,
Firas
