Implementing initial weights and significant feedback delays in a NARNET

 Hi. I’m trying to understand the concepts behind finding training strategies for NARNETs that can make as good predictions as possible. What I want to create is a script that I can feed any time series to, regardless of how it looks, and then find the best training design for it. This is the code I have at the moment:

 

T = simplenar_dataset; %example time series
N = length(T); % length of time series

MaxHidden=10; %number of hidden nodes that will be tested

%Attempt to determine Significant feedback delays with Autocorrelation
autocorrT = nncorr(zscore(cell2mat(T),1),zscore(cell2mat(T),1),N-1);
[ sigacorr inda ] = find(abs(autocorrT(N+1:end) > 0.21))

for hidden=1:MaxHidden
    parfor feedbackdelays=1:length(inda)

FD=inda(feedbackdelays);

net = narnet( 1:FD, hidden );

[ Xs, Xsi, Asi, Ts ] = preparets( net, {}, {}, T );
ts = cell2mat( Ts );

net.divideFcn ='divideblock'; %Divides the data using divide block

net.trainParam.min_grad=1e-15;
net.trainParam.epochs=10000;

rng( 'default' )
[ net tr Ys Es Af Xf ] = train( net, Xs, Ts, Xsi, Asi);
NMSEs = mse( Es ) /var( ts,1 )% Mean squared error performance function
performanceDivideBlockNMSEs(hidden,feedbackdelays)=NMSEs;

      end
  end

First off: Is this the correct way of implementing the statistically significant feedback delays?

 

And if the “net.divideFcn ='divideblock'” line is left uncommented as in the code now I get an error message in the loop saying “Attempted to access valInd(0); index must be a positive integer or logical.” which I’m not sure what is causing.

 

And I’ve heard people say that you should “try different initial weights”, how do I do that, is it the rng command I need to change?

 

The idea here is then that I find the address of the best performing net in the performanceDivideBlockNMSEs matrix so I can retrain a closed net with those settings and make predictions, but for now I’m just focusing on the open net.

ANSWER

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1. Unfortunately, the form of NNCORR that you are using is BUGGY!

   PROOF:
   a. plot(-(N-1):N-1, autocorrT)
   b. minmax(autocorrT) = [ -2.3082  1.0134 ]
   c. sigacorr  = ones(1,41)

2. BETTER SOLUTION: Use the Fourier Method

   za = zscore(a,1); zb = zscore(b,1); % a,b are double (i.e., not cells)
   A  = fft(za);      B = fft(zb);

   CSDab         = A.*conj(B);            % Cross Spectral Density
   crosscorrFab = ifft(CSDab);            % F => Fourier method
   crosscorrFba = conj(crosscorrFab);

3. You might wish to compare this with the NNCORR documentation options

   help nncorr
   doc nncorr

% The optional FLAG determines how nncorr normalizes correlations.
%     'biased'     - scales the raw cross-correlation by 1/N.
%     'unbiased' - scales the raw correlation by 1/(N-abs(k)), where k 
%                       is the index into the result.
%     'coeff'       - normalizes the sequence so that the correlations at 
%                       zero lag are identically 1.0.
%     'none'      - no scaling (this is the default).

 crosscorrBab = nncorr( za, zb, N-1, 'biased' );   % B ==> "b"iased
 crosscorrNab = nncorr( za, zb, N-1, 'none' )/N;   % N ==> "n"one

 crosscorrUab  = nncorr( za, zb, N-1, 'unbiased' ); % U ==> "u"nbiased
 crosscorrtMab = nncorr( za, zb, N-1 );             % M ==> "m"issing flag

 % crosscorrCab = nncorr( za, zb, N-1, 'coeff' ); ERROR: BUG

You

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