“归一化均方误差”说的是什么？

Question

I know that mean squared error is a public and popular metric to evaluate the efficiency of the model and architecture. Also, it is the tool to evaluate the result in such if, the MSE did not arrive well, by tunning the model it is expected to have a better result. BUT, What about NMSE which stands for Normalized mean squared error . How it can be interpreted? I mean, how can I interpret the result that comes out? I have used my own function to get it, which is here:

def rmse(predictions, targets):

    differences = (predictions - targets)/targets                      

    differences_squared = differences ** 2                    

    mean_of_differences_squared = differences_squared.mean()  

    rmse_val = np.sqrt(mean_of_differences_squared)           

    return rmse_val 

Answer 1

Althought this is not a programming question and it should be addressed more to a statistics /data science platform, we can say that the normalized MSE gives you an idea about the error independently of the absolute mean value.

Consider two cases where you have a range of values form 1 to 100 and another from 100 to 100000. If you just calculate the MSE the variance will appear bigger for the range of 100 to 100000 because the absolute values of the measurements are just larger. But as a fraction or percentage of the actual values the range 1 to 100 might have higher variance.

The normalized MSE allows you to compare the error for sets with vary different value ranges.