I'm using the Matlab Neural Network toolbox for a regression problem (twelve inputs, one target). My target has a high dynamic range and is strongly non-gaussian. So far I've solved this by a log-transformation, but as an alternative I'm exploring if a different error function than the standard mean square error would be of use.
The Matlab Neural Network toolbox comes with four built-in "performance" functions:
>> help nnperformance Neural Network Toolbox Performance Functions. mae - Mean absolute error performance function. mse - Mean squared error performance function. sae - Sum absolute error performance function. sse - Sum squared error performance function.
In my understanding, such a performance function is a cost function. But as a cost function is simply something to be minimised, what is the difference between Mean absolute error and Sum absolute error in practice? Similarly, what is the difference between Mean squared error and Sum squared error? Shouldn't those be the same?
The documentation for the different functions is of no use. In fact, the documentation for mse and sse is identical apart except for one word.