I would like to share with you how I approached a nonlinear regression problem (2 inputs, one output), and have your advice.
After some quick readings I settled for a network with one single hidden layer with the tansig transfer function and purelin for the output, as it seems to be the most common approach for such problems.
I used trainbr in order to automatically determine the regularization parameter. However, I didn't find out how to automatically determine the number of hidden neurons (which should normally be possible in the Bayesian framework if I'm not msitaken). So I couldn't conflate the training and validation sets ; I kept the validation set to evaluate architectures of increasing amounts of neurons.
So within one for loop going from 1 to 20, I trained networks with 1 to 20 neurons in the hidden layer. Then, I applied them on the validation set and computed the mean squared error.
First question : is this the most appropriate way to do? Would you have done differently?
The MSE keeps getting smaller as the number of neurons increase. I stopped at 20 as there seems to have no real benefits in going further. Then, I applied the 2-20-1 net to the test set, and got a very very small MSE of 4e^-6, and a correlation of 0.99999 between the test labels and the output of the network.
Second question : isn't it suspicious to get such a high performance? What do you think about this?
I'll be looking forward to your responses in order to validate or dismiss my approach.
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TRAINBR does not use a validation set. Therefore I am not quite sure what you are doing.
Are you using TRAINBR's default 15% test subset as a holdout (NO validation stopping) validation subset for choosing the best of multiple designs?
Then , I assume you have a third holdout subset that you use for testing, i.e., to use the "best net" performance on the test set as an unbiased estimate of it's performance on non-design operational data.
My advice is to use the smallest number of hidden nodes, H, that will yield a degree-of-freedom-adjusted coefficient of determination exceeding 99%. Use a double loop with ~ 10 random weight initialization designs (inner loop) for each value of H (outer loop). Ten values of h should be sufficient.
I have posted many double loop designs in ANSWERS and NEWSGROUP.
If you have more questions, please include your code with comments.
Hope this helps.
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