Neural Network forecasting Issue
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Hello,
I've created a neural network to fit a certain (simple) input-output relationship. When I look at the time-series responses plot using the nntrain gui the predictions seem quite adequate, however, when I try to do out of sample prediction the results are nowhere close to the function being modelled.
I've googled this problem extensively and messed around with my code to no avail, I'd really appreciate a little insight into what I've been doing wrong.
I've included a minimal working example below.
A = 1:1000; B = 10000*sin(A); C = A.^2 +B;
Set = [A' B' C'];
input = Set(:,1:end-1);
target = Set(:,end);
inputSeries = tonndata(input(1:700,:),false,false);
targetSeries = tonndata(target(1:700,:),false,false);
%
inputSeriesVal = tonndata(input(701:end,:),false,false);
targetSeriesVal = tonndata(target(701:end,:),false,false);
%
inputDelays = 1:2;
feedbackDelays = 1:2;
hiddenLayerSize = 5;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize);
%
[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);
net.divideFcn = 'divideblock'; % Divide data in blocks
net.divideMode = 'time'; % Divide up every value
% Train the Network
[net,tr] = train(net,inputs,targets,inputStates,layerStates);
Y = net(inputs,inputStates,layerStates);
% Prediction Attempt
delay=length(inputDelays); N=300;
inputSeriesPred = [inputSeries(end-delay+1:end),inputSeriesVal];
targetSeriesPred = [targetSeries(end-delay+1:end), con2seq(nan(1,N))];
netc = closeloop(net);
[Xs,Xi,Ai,Ts] = preparets(netc,inputSeriesPred,{},targetSeriesPred);
yPred = netc(Xs,Xi,Ai);
perf = perform(net,yPred,targetSeriesVal);
figure;
plot([cell2mat(targetSeries),nan(1,N);
nan(1,length(targetSeries)),cell2mat(yPred);
nan(1,length(targetSeries)),cell2mat(targetSeriesVal)]')
legend('Original Targets','Network Predictions','Expected Outputs')
end
I'd appreciate any insight into what I'm doing wrong,
Regards, James
1 个评论
Greg Heath
2013-2-4
Plot A, A.^2, B and C.
1. Terms differ by many orders of magnitude
2. The dominant term A.^2 is not stationary.
3. There are no explicit lags in your equation
4. Find more appropriate time series data in the documentation.
Greg
采纳的回答
Shashank Prasanna
2013-2-3
You are using the wrong type of network for your problem.
Essentially you are trying to fit a function which is completely uncorrelated with itself, and you have no reason to use an Autoregressive network at all. You can choose a classical feedforward network to fit a function and forecast, it will do a much better job.
If you have a function where
C(n) = f(C(n-1),C(n-2),...)
NARX will make more sense.
3 个评论
James Donovan
2013-2-3
Shashank Prasanna
2013-2-3
James, there are several concerns. Firstly this is not an appropriate netowrk for you data as I mentioned, secondly with a choice of network you HAVE TO play around with the number of nodes and delays - this is more art than science.
Ex1: Make the following change for descent prediction for atleast 30steps
rng(0)
inputDelays = 1:10;
feedbackDelays = 1:10;
hiddenLayerSize = 30;
Note: I mention again, you have NO serial autocorrelation, there is NO reason what so ever for the network to keep predicting perfectly for ever. Try an open loop architecture such as FITNET. Its just a model, and it has limitations.
Ex2: I have concerns about your your data. It is not stationary and that sometimes poses problems. See how the network give you near perfect prediction here: Change
C = B;
and
rng(0);
inputDelays = 1:10;
feedbackDelays = 1:10;
hiddenLayerSize = 20;
Again I can emphasize enough, the tools are only good if you use them appropriately. Only the right tool with the right configuration may give you desired results. Please used the rng(0) so that you can reproduce my results. It sets the random seeds.
James Donovan
2013-2-5
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