How to predict future responses y(t + 1) from the training of a narxnet network with past data of x (t) and y (t)? (NARXNET)

Greetings,

I hope someone could help me with the next question:

As input variables for the NARXNET (time series) type neural network I have the following data (cells arrays):

INPUTS: x(t): 1 x 55, each column with 18 x 1. The 18 variables are entries.

OUTPUTS: y(t): 1 x 55, each column with 6 x 1. The 6 variables are outputs.

The 18 input variables are different from 6 output variables. There have high correlations between them. I have a model using a step-by-step regression (multiple) to compare this results with the final results of the NARXNET net. I'm using MSE as statistical error measurement between methods.

I wish to predict Y(1) only by using a input matrix x(t): 1 x 55 (each column 18 x 1 variables).

How could I evaluate the network (net) created using a matrix x(t):1 x 55 (each column 18 x 1 variables) different from the one used during training?

%-------------------------TRAINING RESULTS------------- (ANY COMMENTS ABOUT THIS RESULTS?)

I'm using the following code from the Matlab examples in ntstool.

This is the code (any correction and suggestion will be welcome):

%---------------------------------------------ANN FORECASTING--------------------------------------------

inputSeries = INPUTS; %x(t): 1 x 55, each column with 18 x 1. The 18 variables are entries.

targetSeries = OUTPUTS; %y(t): 1 x 55, each column with 6 x 1. The 6 variables are outputs.

%Bayesian model

trainFcn = 'trainbr';

% Create a Nonlinear Autoregressive Network with External Input

inputDelays = 1:0;

feedbackDelays = 1:1;

hiddenLayerSize = 30;

net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'open',trainFcn);

%view(net)

[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);

% Set up Division of Data for Training, Validation, Testing

net.divideFcn = 'divideblock';

net.divideMode = 'value';

net.trainParam.epochs = 10000;

net.trainParam.goal = 0;

net.trainParam.lr = 0.001;

net.divideParam.trainRatio = 85/100;

net.divideParam.valRatio = 15/100;

net.divideParam.testRatio = 15/100;

%MSE

net.performFcn = 'mse';

% Train the Network

[net,tr] = train(net,inputs,targets,inputStates,layerStates);

% Test the Network

outputs = net(inputs,inputStates,layerStates);

errors = gsubtract(targets,outputs);

performance = perform(net,targets,outputs)

% View the Network

view(net)

% Plots

% Uncomment these lines to enable various plots.

% figure, plotperform(tr)

% figure, plottrainstate(tr)

% figure, plotregression(targets,outputs)

% figure, plotresponse(targets,outputs)

% figure, ploterrcorr(errors)

% figure, plotinerrcorr(inputs,errors)

% Closed Loop Network

% Use this network to do multi-step prediction.

% The function CLOSELOOP replaces the feedback input with a direct

% connection from the output layer.

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc,xic,aic,tc] = preparets(netc,inputSeries,{},targetSeries);

yc = netc(xc,xic,aic);

closedLoopPerformance = perform(netc,tc,yc)

% Early Prediction Network

% For some applications it helps to get the prediction a

% timestep early.

% The original network returns predicted y(t+1) at the same

% time it is given y(t+1).

% For some applications such as decision making, it would

% help to have predicted y(t+1) once y(t) is available, but

% before the actual y(t+1) occurs.

% The network can be made to return its output a timestep early

% by removing one delay so that its minimal tap delay is now

% 0 instead of 1. The new network returns the same outputs as

% the original network, but outputs are shifted left one timestep.

%nets = removedelay(net,1);

nets=net;

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs,xis,ais,ts] = preparets(nets,inputSeries,{},targetSeries);

ys = nets(xs,xis,ais);

earlyPredictPerformance = perform(nets,ts,ys)

Answer 1

[Greg Heath]

YOU DO NOT HAVE X and Y !!!

YOU HAVE X and T where

T = Ydesired

Hope this helps

Thank you for formally accepting my answer

Greg

[Cesar Diaz]

Hi Greg, thanks for the answer.

But, how I could send a input matrix x(t), different from the training matrix?. Over the last code, do you could help me with that?.

So, the forecasted responses are:

yc = netc(xc,xic,aic); %CLOSED LOOP

ys = nets(xs,xis,ais); %ONE STEP AHEAD

How I could make a new forecast from:

outputs = net(inputs,inputStates,layerStates); %OPENED LOOP

I need to load a new x(t) matrix for make a forecast T(t).

Thanks Greg.