Noob question: why should we normalize test data with mean and std from training data? • /r/MachineLearning

Nah. It's only really required for things like Neural Networks where it keeps the gradient descent of features in the space where gradient descent does best, and for Linear/Logistic Regression where it also isn't really required, but makes the weights interpretable as feature importance/contribution to the prediction. For things like Random Forest, which are based on decision trees, they'll find a split anywhere, it doesn't matter how the features are scaled. For stuff like Nearest Neighbours, it can be important, or it can hurt. This is because normalisation is like saying all features are equally important, which isn't necessarily true. It could be the case that you've got spatial information in a rectangular space, and so normalising is favouring the small axis of that rectangle over the other axis.