I have to implement a Partial Least Squares (PLS) where my data features are in the X matrix (N,P) and my dependent variable is Y (Nx1). In PCA as in other Machine Learning methods, one usually needs to standardize the X features before passing the algorithm (demean and scaled to have unit standard deviation). Now say I have standardized X. If I use PLS (e.g. from sklearn), I obtain different results if I scaled Y or not. By default, PLSRegression (https://scikit-learn.org/stable/modules/generated/sklearn.cross_decomposition.PLSRegression.html) scale both X and Y. However, from here https://stat.ethz.ch/pipermail/r-help/2004-February/045457.html it seems it is not necessary to rescale Y. Since PLS essentially looks at the most important directions of the matrix COV(X,Y), I understand that scaling Y would be appropriate so that Y has the same "importance" as the features, but after all Y is somehow more important than the feature as it is what I am trying to describe while performing dimension reduction on X. Moreover, I am not sure I want my Y to be reduced to unit standard deviation, as my Y is stock returns.
Somebody knows more about the point?
