Neural Network : Poor Result

Hello,

I was trying to simulate MATLAB's NN functions before testing my network. I was training y = x1+x2.

But see how it performed,

>> net = newfit([1 2 3 4 5 0 1 2 5;1 2 3 4 5 1 1 1 1],[2 4 6 8 10

0 2 3 6],15);

>> net = train(net,[1 2 3 4 5 0 1 2 5;1 2 3 4 5 1 1 1 1],[2 4 6 8

10 0 2 3 6]);

>> sim(net,[1;4])

ans =

   12.1028

>> sim(net,[4;4])

ans =

    8.0000

>> sim(net,[4;1])

ans =

    3.0397

>> sim(net,[2;2])

ans =

    5.1659

>> sim(net,[3;3])

ans =

   10.3024

Can anyone explain what is wrong with these training data? Is it not enough to estimate y = x1+x2 ? Or it just over-specialized?

Answer 1

[Greg Heath]

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PTRN = [1 2 3 4 5 0 1 2 5; 1 2 3 4 5 1 1 1 1]

TTRN = [2 4 6 8 10 0 2 3 6]

PTST = [ 1 4 4 2 3 ; 4 4 1 2 3 ]

[ I NTRN ] = SIZE(PTRN) % [ 2 9 ] [ O NTRN ] = SIZE(TTRN) % [ 1 9 ]

DID YOU MAKE A CONTOUR PLOT OF TTRN VS PTRN?

DID YOU OVERLAY THE POINTS OF PTST ON THE CONTOUR PLOT?

NEQ = NTRN*O % 9 NW = (I+1)*H+(H+1)*O % 30 + 11 = 41

YOU HAVE ONLY 9 TRAINING EQUATIONS FOR 41 UNKNOWN WEIGHTS.

DON'T EXPECT MUCH WHEN YOU USE THIS NET FOR NONTRAINING DATA

UNLESS:

1. YOU USE STOPPED TRAINING WITH A VALIDATION SET AND/OR

2. YOU USE REGULARIZATION VIA TRAINBR AND/OR

3. YOU REDUCE H AND/OR

4. YOU INCREASE NTRN

WHAT DID YOU GET FOR

MSETRN00 = VAR(TTRN)

YTRN = SIM(NET,PTRN)

ETRN = TTRN-YTRN

MSETRN = MSE(ETRN)

R2TRN = 1-MSETRN/MSETRN00

HOPE THIS HELPS.

GREG

[Greg Heath]

WHEN YOU MAKE UP EXAMPLES, TAKE THEM FROM SAMPLING A SMOOTH FUNCTION.

TO BE MORE REALISTIC YOU CAN ADD SOME RANDOM NOISE CONTAMINATION.

MAKE SURE NEQ >= NW (PREFERABLY NEQ >> NW)UNLESS YOU ARE TESTING

WAYS TO MITIGATE OVERTRAINING AN OVERFIT NET.

HOPE THIS HELPS.

GREG

P.S. SEE THE OVERFITTING SECTION OF THE COMP.AI.NEURAL-NETS FAQ