Differences between QuantileTransformer and PowerTransformer

Question

In sklearn, the document of QuantileTransformer says

This method transforms the features to follow a uniform or a normal distribution

the document of PowerTransformer says,

Apply a power transform featurewise to make data more Gaussian-like

It seems both of them can transform features to a gaussian/normal distribution. What are the differences in terms of this aspect and when to use which?

Answer 1

It is confusing terminology that they use because Gaussian and normal distribution are actually the SAME.

QuantileTransformer and PowerTransformer are both non-linear.

To answer your question about what exactly is the difference it is this according to https://scikit-learn.org :

"QuantileTransformer provides non-linear transformations in which distances between marginal outliers and inliers are shrunk. PowerTransformer provides non-linear transformations in which data is mapped to a normal distribution to stabilize variance and minimize skewness. "

Source and more info here: https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#:~:text=QuantileTransformer%20provides%20non%2Dlinear%20transformations,stabilize%20variance%20and%20minimize%20skewness .

Answer 2

The main difference is PowerTransformer() being parametric and QuantileTransformer() being non-parametric. Box-Cox or Yeo-Johnson will make your data look more 'normal' (ie less skewed and more centered) but it's often still far from the perfect gaussian. QuantileTransformer(output_distribution='normal') results usually look much closer to gaussian, at the cost of distorting linear relationships somewhat more. I believe there's no rule of thumb to decide which one would work better in a certain case, but it's worth noting you can select an optimal scaler in a pipeline when doing eg GridSearchCV() .