In evaluating a neural net, should NMSE be based only on test subset of data?

In answers like this, Greg Heath suggests using the normalized mean square error, NMSE, to compare the performance of different neural networks and pick the best one.

I have been calculating NMSE from all samples in the training set t and prediction y,

[net tr y e ] = train(net,x,t); % Train network
vart1  = var(t',1);
% MSE for a naive constant output model 
% that always outputs average of target data
MSE00 = mean(vart1);
NMSE = mse(t-y)/MSE00; % Normalize

That includes the training samples, and so may favor models that fit the training data well but not new data. In order to choose the most robust model, should I calculate NMSE from the test samples only?

iTest = tr.testInd; % Index to the samples that were set aside for testing
NMSE_test_only = mse(t(:,iTest)-y(:,iTest))/MSE00; % Only use test samples

Answer 1

[Greg Heath]

For serious work I calulate FOUR values of NMSE:

1.70% Training

2.15% Validation

3.15% Test

4.100% All

for 10 (typically) random data divisions & initial weights and try to use as few hidden nodes as possible.

Hope this helps

Greg

[KAE]

Once you have those 4 values of NMCE, do you pick the 'best' number of neurons (or whatever network feature you are optimizing) based on the net which has the highest test NMSE, averaged over the 10 trials?

[Greg Heath]

Typically, I try to minimize the number of hidden nodes subject to the constraint NMSEtrn <= 0.01 . I then rank those nets according to NMSEval and NMSEtst.

Details can be found in my NEWSGROUP and ANSWERS posts.

Greg