Neural Network result offset by one

I am learning the Neural Networks toolbox and I worked through a simple example using narxnet to predict the output of a sine function:

proffset = 5;               % target offset to train for prediction
tdelay = 2;                 % length of delay line
x = [1:tstep:15];           % create the example function
y = 2*sin(x)+1;             %  y = f(x(t)), x(t)=t
xo = x(1:end-proffset);     % training inputs, x(t)
yo = y(proffset+1:end);     % training targets, y(t-T)
net = narxnet(1:tdelay,1:tdelay,10);  % default values
[Xs,Xi,Ai,Ts,Ew,tshift] = preparets(net,num2cell(xo),{},num2cell(yo));
net = train(net,Xs,Ts,Xi,Ai);
[yn, xn, an] = net(Xs,Xi,Ai);
plot(xo(tdelay+1:end),cell2mat(yn),'o-g');

This works fine. The outputs match the targets very closely, as expected for a simple function.

However, when I use my real data in this code framework, the output results are clearly shifted by -1, even though the number of outputs is correct (i.e., number of outputs = number of targets - length of delay line).

The example seems very straightforward, and I can't figure out why "real" data would produce this kind of behavior. What can cause this kind of offset? Thank you!

Answer 1

[Greg Heath]

1. Since I always use

    a. t and y to denote target and output
    b. subscripts "o" and "c" to denote "o"penloop
       and "c"loseloop,

I had to change notation to prevent my confusion.

2. What does the pr in proffset represent?

3. Shouldn't your comment concern training input x(t) and training target y(t+T) (instead of y-T) so that x(1) predicts y(1+T) ? I think this may have caused your confusion.

4. The default 'dividerand' causes interpolation (at (sometimes VERY) nonconstant timesteps). To get a good understanding use the diff function to determine the spacings among the validation and test data for this simple example:

 [trnind valind tstind]= dividerand(100,0.7,0.15,0.15);
 valspacing  = diff(valind)
 testspacing = diff(tstind)

 Surprised?

5. For unbiased timeseries prediction

 testInd = [ Ntrn + Nval + 1: N ]

This can be accomplished in many ways

a. Divideblock: [ Ntrn, Nval, Ntst ] %Includes Nval = 0
b. Divideint,divideind or dividerand on 1:Ntrn+Nval

Obviously, only divideblock provides accurate spacing.

 close all, clear all, clc, plt=0,  tic

 dx = 0.1, x0 = [ 1: dx: 15 ]; t0 = 2*sin( x0 ) + 1;
 [ I N0 ] = size(x0), [ O N0 ] = size(t0) % [ 1 141 ]
 offset   = 5,  N  =  N0 - offset         % 136
 x = x0(1:end - offset );  t = t0(offset + 1 : end );
 X = con2seq(x);  T = con2seq(t);

 d=2, ID = 1:d, FD = 1:2, H = 10 % NARXNET defaults
 neto = narxnet;
 % neto.divideFcn = 'divideblock';  % For prediction
 [ Xo, Xoi, Aoi, To  ] = preparets( neto, X, {}, T );
 to=cell2mat(To);varto=var(to,1) % 2.0492 Reference MSE

% Desire MSEo/varto <= 0.005 before closing loop

 Ntrials = 12
 rng('default')
 for i =1:Ntrials
    state(i) = rng;
    neto = configure(neto, Xo, To);
[neto tro Yo Eo Xof Aof]=train(neto,Xo,To,Xoi,Aoi);
    % [Yo Xof Aof ] = net(Xo,To,Xoi,Aoi);
    % Eo = gsubtract(To,Yo)
    NMSEo(i) = mse(Eo)/varto;
end
 [ minNMSEo imin] = min(NMSEo)  % [  1.8972e-06  8 ]
 result = NMSEo
 % result = 0.022016 0.0024273 0.0026271 3.2378e-5
 %          0.010759 0.15988   0.0074602 1.8972e-6   
 %          0.000851 0.79191   0.0008976 0.0064785

Hope this helps.

Thank you for formally accepting my answer

Greg

[M. A. Hopcroft]

Hello Greg,

Thank you for your reply. The solution was basically to keep going. I had attempted to use the default settings for the tools in the NN toolbox to validate the NN workflow. This works fine for simple examples. My real signals, however, are too complex to give good results with the default settings. It appears that default network was so poorly suited for the task that it was essentially estimating each output as [approximately] the previous input. After I did some work to optimize the network (estimate appropriate delay line length and number of hidden layers) the results improved dramatically. Your reply here was very helpful, as are your other posts on NN topics in this forum. I appreciate your time.

Matt