Understanding Mean Squared Error in Neural Networks

[hisham.i]

In neural network the learning algorithm ends when the mean squared error value is less than or equal to a value we have precised.
But i don't understand why we are comparing with the mean squared error and not the mean error?
What does the mean squared error represent?

 

[JaredJames]

I'm not sure of the exact answer you require, but if it's anything like using RMS values it's pretty straight forward.

Let's say you have two error values: -1 and 1

The mean error value is 0.
The mean squared error is 1.

If I remember correctly, it is because you have alternating positive and negative values and no matter what you do you end up with 0 as the mean if you simply take the average of the exact values.

For example, with alternating current of 230V (UK standard supply) you have a sin wave with a maximum of +320V and a minimum of -320V. If you average these values you get an average voltage out of your wall socket of 0V - this is of no use to you.

So you use an RMS (Root Mean Squared) value to get a useful value.

In this case you have +320V and -320V. So you square them (+320² and -320V-²).
Add the squared values together (+320V²+-320V²).
Square root them and then take the mean (Sqrt(+320V²+-320V²))/2.

This then gives you the RMS voltage. For the UK this is ~230V.

So by using a value such as your "squared error" you get a useful answer instead of 0 every time.

 

[Phrak]

In neural network the learning algorithm ends when the mean squared error value is less than or equal to a value we have precised.
But i don't understand why we are comparing with the mean squared error and not the mean error?
What does the mean squared error represent?

I'm sure you mean the root mean squared error meaning the root of the averaged sum of the squared differences from the averaged value.