I read all about pros and cons of RMSE vs. other absolute errors namely mean absolute error (MAE). See the the following references:
- MAE and RMSE — Which Metric is Better?
- What's the bottom line? How to compare models
- Or this nice blogpost, or this question in stats.stackexchange containing interesting responses, and this one in datascience.stackexchange
Still I can not get my head around something about RMSE:
Scenario: Let's say we have a regressor for predicting house prices with a MAE of 20.5\$ and a RMSE of 24.5\$. Based on MAE, I can certainly interpret that the average difference between the predicted and the actual price is 20.5\$. How can I interpret RMSE? Can we still safely say the predicted and the actual price are off by 24.5\$ at the same time base on RMSE (upper-bound of prediction error)?
In the first medium post, it says:
RMSE does not describe average error alone and has other implications that are more difficult to tease out and understand.
It confuses me a little. And I could not find any reliable reference to also clearly state that one can safely interpret RSME as one does MAE. Is RMSE is simply a only mathematically more convenient for optimization etc., and we are better off with MAE for the interpretation?
Any detailed explanation is highly appreciated.