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 seriesMaxHidden=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 blocknet.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.
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- 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 should find that B & N are equivalent, Similarly for U & M.
Therefore, there are really only 2 NNCORR options to consider: Biased and Unbiased.
It is instructive to overlay the plot combinations F&B, F&U, B&U. Most notable is that for lags greater than ~N/2 the three are, in general, quite different. Although the differences are much less for lags < N/2, I recommend using the Fourier method or one of the correlation functions from other toolboxes.
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