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My question is about the properties and proper use of "Ordered quantile normalization" from the paper titled “Ordered quantile normalization: a semiparametric transformation built for the cross-validation era”. The formula of the transformation is a little difficult to understand. The transformation is available in R package called bestNormalize. As far as I understood, it fits a function to transform a non-normal distribution to normal in a numerical vector. The transformation maintains ranks of the numbers in a vector. Then the fit information (parameter values) could be saved and used by predict function in the package to transform a new vector to the normal distribution (or close to normal). Since it is meant to be used in machine learning, my question is whether the transformation results in any leak of information from the training set to test set via the transformation or across different observations (within train or test sets). Also doesn’t this process force the numbers/values in the test set to be too similar to the training set and thus making the performance of a classification/regression task too easy (compared to using the original data distribution) due to a sort of bias added by the transformation? Since the transformation does not change the rank of data, are transformed values interpretable?

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Based on an answer I got from the author, it appears that the transformation does not add any bias by itself to the learning process of a machine learning pipeline when the training ans test sets are independent. The transformed values are not however as straightforward to interpret as the original values, thus it is suggested to plot the transformed values against the original values for better interpretation (as also available in the package vignette). The reason is that the transformation does not preserve the scale of the original data as it is also discussed in https://github.com/petersonR/bestNormalize/issues/1

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