Function approximation: Neural network great
Function approximation: Neural network great ‘on paper’ but when simulated results are very bad?
I need some help with NN because I don’t understand what happened. One hidden layer, I=4, H=1:20, O=1. I run each net architecture 10 times with different initial weights (left default initnw). I have in total 34 datasets which were divided 60/20/20 when using Levenberg-Marquadt algorithm. Mse_goal = 0.01*mean(var(t’,1)), i calculate NMSE and R², choose best R², for that check performance of each subsample, check regression plots, check rmse. R² is usually around 0,95; R for each subset 0,98… But when I simulate network with completely new set of data, estimations deviate quite a lot. It is not because of extrapolation. Data are normalized with mapminmax, transfer functions tansig, purelin.
Trainbr was my first choice actually, since I have small dataset and trainbr doesn’t need validation set (Matlab2015a), but it is awfully slow. I ran a net with trainbr and we are talking hours versus minutes with trainlm.
I’ve read a ton of Greg Heath’s posts and tutorials and found very valuable information there, however, still nothing. I see no way out.
% Solve an Input-Output Fitting problem with a Neural Network
% Script generated by Neural Fitting app
% Created 09-Aug-2016 18:33:13% This script assumes these variables are defined:
%
% MP_UA_K - input data.
% UA_K - target data.close all, clear allload varUA_Kx = MP_UA_K;
t = UA_K;var_t=mean(var(t',1)); %t variance[inputs,obs]=size(x); %hiddenLayerSize = 20; %max number of neurons
numNN = 10; % number of training runsneurons = [1:hiddenLayerSize]';
training_no = 1:numNN;
obs_no = 1:obs;nets = cell(hiddenLayerSize,numNN);
trainOutputs = cell(hiddenLayerSize,numNN);
valOutputs = cell(hiddenLayerSize,numNN);
testOutputs = cell(hiddenLayerSize,numNN);
Y_all = cell(hiddenLayerSize,numNN);
performance = zeros(hiddenLayerSize,numNN);
trainPerformance = zeros(hiddenLayerSize,numNN);
valPerformance = zeros(hiddenLayerSize,numNN);
testPerformance = zeros(hiddenLayerSize,numNN);
e = zeros(numNN,obs);
e_all = cell(hiddenLayerSize,numNN);
NMSE = zeros(hiddenLayerSize,numNN);
r_train = zeros(hiddenLayerSize,numNN);
r_val = zeros(hiddenLayerSize,numNN);
r_test = zeros(hiddenLayerSize,numNN);
r = zeros(hiddenLayerSize,numNN);
Rsq = zeros(hiddenLayerSize,numNN);for j=1:hiddenLayerSize % Choose a Training Function
% For a list of all training functions type: help nntrain
% 'trainlm' is usually fastest.
% 'trainbr' takes longer but may be better for challenging problems.
% 'trainscg' uses less memory. Suitable in low memory situations.
trainFcn = 'trainbr'; % Bayesian Regularization backpropagation. % Create a Fitting Network
net = fitnet(j,trainFcn); % Choose Input and Output Pre/Post-Processing Functions
% For a list of all processing functions type: help nnprocess
net.input.processFcns = {'removeconstantrows','mapminmax'};
net.output.processFcns = {'removeconstantrows','mapminmax'}; % Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
% podaci su sortirani prema zavisnoj varijabli, cca svaki tre?i dataset je
% testni
net.divideFcn = 'divideind'; % Divide data by index
net.divideMode = 'sample'; % Divide up every sample
net.divideParam.trainInd = [1:3:34,2:3:34];
% net.divideParam.valInd = [5:5:30];
net.divideParam.testInd = [3:3:34]; mse_goal = 0.01*var_t; % Choose a Performance Function
% For a list of all performance functions type: help nnperformance
net.performFcn = 'mse'; % Mean Squared Error
net.trainParam.goal = mse_goal; % Choose Plot Functions
% For a list of all plot functions type: help nnplot
net.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...
'plotregression', 'plotfit'}; for i=1:numNN
% Train the Network
net = configure(net,x,t);
disp(['No. of hidden nodes ' num2str(j) ', Training ' num2str(i) '/' num2str(numNN)])
[nets{j,i}, tr{j,i}] = train(net,x,t); y = nets{j,i}(x); e (i,:) = gsubtract(t,y);
e_all{j,i}= e(i,:); trainTargets = t .* tr{j,i}.trainMask{1};
%valTargets = t .* tr{j,i}.valMask{1};
testTargets = t .* tr{j,i}.testMask{1}; trainPerformance(j,i) = perform(net,trainTargets,y);
%valPerformance(j,i) = perform(net,valTargets,y);
testPerformance(j,i) = perform(net,testTargets,y); performance(j,i)= perform(net,t,y); rmse_train(j,i)=sqrt(trainPerformance(j,i));
%rmse_val(j,i)=sqrt(valPerformance(j,i));
rmse_test(j,i)=sqrt(testPerformance(j,i));
rmse(j,i)=sqrt(performance(j,i)); % outputs of all networks
Y_all{j,i}= y; trainOutputs {j,i} = y .* tr{j,i}.trainMask{1};
%valOutputs {j,i} = y .* tr{j,i}.valMask{1};
testOutputs {j,i} = y .* tr{j,i}.testMask{1}; [r(j,i)] = regression(t,y);
[r_train(j,i)] = regression(trainTargets,trainOutputs{j,i});
%[r_val(j,i)] = regression(valTargets,valOutputs{j,i});
[r_test(j,i)] = regression(testTargets,testOutputs{j,i}); NMSE(j,i) = mse(e_all{j,i})/mean(var(t',1)); % normalized mse % coefficient of determination
Rsq(j,i) = 1-NMSE(j,i); end [minperf_train,I_train] = min(trainPerformance',[],1);
minperf_train = minperf_train';
I_train = I_train';% [minperf_val,I_valid] = min(valPerformance',[],1);
% minperf_val = minperf_val';
% I_valid = I_valid'; [minperf_test,I_test] = min(testPerformance',[],1);
minperf_test = minperf_test';
I_test = I_test'; [minperf,I_perf] = min(performance',[],1);
minperf = minperf';
I_perf = I_perf'; [maxRsq,I_Rsq] = max(Rsq',[],1);
maxRsq = maxRsq';
I_Rsq = I_Rsq'; [train_min,train_min_I] = min(minperf_train,[],1);% [val_min,val_min_I] = min(minperf_val,[],1); [test_min,test_min_I] = min(minperf_test,[],1); [perf_min,perf_min_I] = min(minperf,[],1); [Rsq_max,Rsq_max_I] = max(maxRsq,[],1);endfigure(4)
hold on
xlabel('observation no.')
ylabel('targets')
scatter(obs_no,trainTargets,'b')
% scatter(obs_no,valTargets,'g')
scatter(obs_no,testTargets,'r')
hold offfigure(5)
hold on
xlabel('neurons')
ylabel('min. performance')
plot(neurons,minperf_train,'b',neurons,minperf_test,'r',neurons,minperf,'k')
hold offfigure(6)
hold on
xlabel('neurons')
ylabel('max Rsq')
scatter(neurons,maxRsq,'k')
hold off% View the Network
%view(net)% Plots
% Uncomment these lines to enable various plots.
%figure, plotperform(tr)
%figure, plottrainstate(tr)
%figure, ploterrhist(e)
%figure, plotregression(t,y)
%figure, plotfit(net,x,t)% Deployment
% Change the (false) values to (true) to enable the following code blocks.
% See the help for each generation function for more information.save figure(4).fig
save figure(5).fig
save figure(6).figif (false)
% Generate MATLAB function for neural network for application
% deployment in MATLAB scripts or with MATLAB Compiler and Builder
% tools, or simply to examine the calculations your trained neural
% network performs.
genFunction(net,'nn_UA_K_BR');
y = nn_UA_K_BR(x);
end% sa?uvati sve varijable iz workspacea u poseban file za daljnju analizu
save ws_UA_K_BR
ANSWER
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% I need some help with NN because I don’t understand what happened. One % hidden layer, I=4, H=1:20, O=1. I run each net architecture 10 times % with different initial weights (left default initnw). I have in total % 34 datasets
Do you mean data points N = 34?It typically takes ~ 10 to 30 data points per dimension to
adequately characterize a distribution. For a 4-D distribution I’d recommend
40 <~ Ntrn <~ 120% which were divided 60/20/20 when using Levenberg-Marquadt
Ntrn = 34-2*round(0.2*34) = 20 Hub = (20-1)/(4+1+1) = 3.2
indicating you really don’t have enough data to adequately characterize a 4-D distribution.
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