do scaling data between 0 and 1, and converting their distribution to a normal distribution changes model's RMSLE

Question

I have a question regarding RMSE and RMSLE:

to create my model, I first scaled all my feature and target data between 0 and 1 and then converted their distribution to normal distribution using gauss rank scaler.

after I fitted a XGBoost model and made prediction on my test sets I used RMSE and RMSLE to evaluate my model.

my question is this:

do I have to convert my data (both predicted and original target values) back to its original form and then calculate RMSE and RMSLE?

or the data scaling and converting mentioned above do not affect the RMSE and RMSLE of the model?

Answer 1

First of all you might not even require to transform the target, depends on use case.

However if you have transformed ( here scaled 0-1), you lose the unit of measurement and then using any evaluation metric for comparison e.g. rmse (or any other in case of regression), it (rmse) here is standard deviation of the residuals calculated on scaled target not on actual values. Thus we must not report this value, however it can be used to comparing across experiments when all experiments uses same underlying data.

For example, based on some features you are predicting age ( say, 0 to 125 yrs). If you scaled age and used as target. Resulting rmse would be over (0-1) scaled target not (0-125 yr).