I have used Bayesian optimization for hyperparameter tuning in a machine learning model. What is the best way to compare the performance of network with and without Bayesian optimization? I found some useful material here, where a comparison was drawn between Random search(grey) and Bayesian Optimization(green) as also shown in below figure. This is exactly what I want to achieve. enter image description here

Script for hyperparameter tuning [MATLAB]:

% Make some data

Daten = rand(100, 3);
Daten(:,3) = Daten(:,1) + Daten(:,2) + .1*randn(100, 1);  % Minimum asymptotic error is .1
[m,n] = size(Daten) ;
% Split into train and test
P = 0.7 ;
Training = Daten(1:round(P*m),:) ; 
Testing = Daten(round(P*m)+1:end,:);
XTrain = Training(:,1:n-1);
YTrain = Training(:,n);
XTest = Testing(:,1:n-1);
YTest = Testing(:,n);
% Define a train/validation split to use inside the objective function
cv = cvpartition(numel(YTrain), 'Holdout', 1/3);
% Define hyperparameters to optimize
vars = [optimizableVariable('hiddenLayerSize', [1,20], 'Type', 'integer');
        optimizableVariable('lr', [1e-3 1], 'Transform', 'log')];
% Optimize
minfn = @(T)kfoldLoss(XTrain', YTrain', cv, T.hiddenLayerSize, T.lr);
results = bayesopt(minfn, vars,'IsObjectiveDeterministic', false,...
    'AcquisitionFunctionName', 'expected-improvement-plus');
T = bestPoint(results)

% Train final model on full training set using the best hyperparameters
net = feedforwardnet(T.hiddenLayerSize, 'traingd');
net.trainParam.lr = T.lr;
net = train(net, XTrain', YTrain');
% Evaluate on test set and compute final rmse
ypred = net(XTest');
finalrmse = sqrt(mean((ypred - YTest').^2))

function rmse = kfoldLoss(x, y, cv, numHid, lr)
% Train net.
net = feedforwardnet(numHid, 'traingd');
net.trainParam.lr = lr;
net = train(net, x(:,cv.training), y(:,cv.training));
% Evaluate on validation set and compute rmse
ypred = net(x(:, cv.test));
rmse = sqrt(mean((ypred - y(cv.test)).^2));
  • $\begingroup$ One thing to reconsider from the example: a "smarter" method like Bayesian searches will take longer per model train than a pure random search; plotting time as the horizontal axis rather than number of iterations may be more honest. (Though with neural nets, likely training time will be the bigger bottleneck.) $\endgroup$
    – Ben Reiniger
    Jan 14, 2020 at 2:45

1 Answer 1


Just measure the out-of-fold-value of your choice, you can add time complexity to the table and than just extract percantage difference.

enter image description here

  • $\begingroup$ Thank you for the useful answer. How to find the default values of the network? This is exactly what I need i.e a comparison between Tuned and Default values. What could be the addition in the above code to determine the default values? $\endgroup$ Jan 15, 2020 at 1:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.