Question
I have seen that MSE, SSE, MAE and SAE are possible training functions of a neural network in Matlab. Does it have relative square error available?
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Expert Answer
Neeta Dsouza
PhD Expert
Answered Nov 20, 2025
The relative (i.e., NORMALIZED) square error is the ratio of the mean-square-error of the model, MSE, to the mean-square-error of the NAIVE CONSTANT-OUTPUT MODEL, MSE00. To minimize the mse of the latter model, the constant output is just the target mean. Correspondingly, MSE00 is just the average target variance.
MSE00 = mean(var(target',1)) Since MSE = mse(target-output); NMSE = MSE/MSE00 % "N"ormalized, or relative, mse.
The coefficient-of-variation or Rsquared, Rsq
Rsq = 1 - NMSE
is the fraction of target variance that is "explained by the model.
I have zillions of posts in both the NEWSGROUP and ANSWERS using the above variables. In some of them I have gone into more detail than I have here.
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