Best way to measure regression accuracy?

Question

I'm asking because classification problems have very concrete metrics like accuracy that are totally transparent to understand.

Whereas regression models seem to have a very large number of possible evaluation strategies and to me at least it is not clear which (if any) of them is as reliable/interpretable as accuracy is in classification problems.

Possible Candidates:

• Regular loss (e.g MAE): MAE is potentially quite interpretable, but again interpretation depends upon distribution statistics which vary across regression problems.
• MAPE/Relative Loss: This is interesting and is potentially decently similar to accuracy. Yet it has obvious draw backs, like the true value being extremely small causing explosion of loss values & there being no incorporation of overall distribution statistics for the output values.
• Chi-squared test: I like the idea of this but I have not seen it used at all for NN regression for some reason. I'm not sure why and I'm curious if people think it would be a good idea to use it for that.
• (adjusted) R^2 coefficient: Another statistic that seems great in theory, but again I see almost never being used for NNs and I'm not sure why. This has the great advantage of being a 'bounded'/'normalized' metric like accuracy and in theory is should be just as interpretable. Why is it not used for NNs?

Answer 1

I've gotten no answer on this, but after some reflection I've come to accept R^2 as regression's analogue to accuracy. I have no idea why it is not used by more people in deep learning, but I recently started using it and it's exactly what I was hoping for! It scales from 0 to 1 and tells you in no uncertain terms how useful the model is and when it becomes unrealistic to improve the model further (e.g. at R^2=0.99). Additionally, R^2=0 when the model starts guessing only the mean of the data, which means it immediately reveals an important and recurring issue in regression which can otherwise go undetected for a while.