Why does the nntool show MSE as the performance function when using Bayesian regularisation (trainbr) both in plot and script?

I know that in Bayesian regularisation a modified performance function is used: a linear combination of squared errors and weights.

However, when I use nntoolbox with Bayesian regularisation or a short script:

net = feedforwardnet(NeurNumber,'trainbr'); [net,tr] = train(net,inputs,targets); y = net(inputs);

I find the automatically created:

net.performFcn = 'mse'

and

tr.pefrormFcn = 'mse'

Also, the plot "performance" gives MSE.

Where is the modified performance function used then? Why does the toolbox show MSE instead? Thank you in advance for answering!

Answer 1

[Sai Pavan]

Hi An St,

I understand that you want to know why the Deep Learning Toolbox shows Mean Squared Error (MSE) as the performance function rather than the Bayesian regularisation function.

It is important to understand that by using the Bayesian regularisation “trainbr” option when building the model, we are modifying the objective function which is a linear combination of squared errors and weights. This regularised objective function will be minimized in an iterative process to control the complexity of the model and prevent overfitting. However, this modified performance function is not directly exposed or accessible in the toolbox's interface or output.

The reason why the performance plot shows MSE is because it provides a standard and widely used metric for assessing the network's performance. It allows you to monitor the training progress and evaluate the convergence and generalization of the network. If you want to assess the effect of Bayesian regularization on the network's performance, you can compare the MSE values obtained with and without Bayesian regularization.

Hope this information will help you understand the difference between objective function and performance measure.

Regards,

Sai Pavan