What kind of RMSE should I choose to show the capability
What kind of RMSE should I choose to show the capability of function approximation with Neural Networks ? This Data set shown below is one of My Data set for function approximation with Neural Network in MATLAB. The left column is the Target vector and the right column is the model output vector. -0.29039678 -0.212428117 0.149798734 0.268486256 0.851351352 0.563358782 -0.694364578 -0.652148947 -0.326624496 -0.468058466 -0.019838988 0.209298441 -0.765669926 -0.828415796 -0.133410006 0.003000269 -0.122484186 -0.073538329 -0.471535366 -0.376903371 0.181426106 0.365548334 0.186889016 0.37947765 -0.260782058 -0.024155069 -0.215353652 -0.371639751 -0.062967222 0.092607096 -0.461759632 -0.56834877 0.074468086 0.154155435 0.624496838 0.529777368 -0.197814836 -0.096543508 -0.247268546 -0.136442585 0.106382978 0.28668492 -0.791259344 -0.718599416 -0.532489936 -0.572352826 -0.006325474 -0.010056861 0.48706153 0.485766679 -0.631397354 -0.619362709 -0.815698678 -0.823629139 0.272857964 0.354840024 0.080506038 0.220713202 and I want to show the capability of my model by calculating the RMSE value between the Target & Output vectors in MATLAB . my question is that what kind of RMSE should I use ? The RMSE obtained by fitlm function lm=fitlm(x,y,'linear'); or RMSE obtained by the formula shown below? RMSE = sqrt(sum((data(:) - estimate (:)).^2) / numel(data)); and if I use the RMSE obtained by fitlm function, Is the RMSE value true ?? because the vector created by lm.predict(x) and my Output vector are different.
Prashant Kumar answered .
2025-11-20
NMSE = MSE/MSE00 = MSE/vart1
where
MSE00 = vart1 = mean(var(target',1))
3. This is not a frivolous choice: NMSE is the fraction of the average target variance that is NOT modelled by the net. Conversely, the "Coefficient of Variation" also known as "R-squared" defined by
Rsq = 1- NMSE
MSEgoal = 0.01*vart1
which yields Rsq = 0.99 (Rsq = 1 is a perfect fit!).