markendrah asked . 2021-07-09

Finding best neural network structure using optimization algorithms and cross-validation

Hi.

I'm using optimization algorithm to find best structure+inputs of a 'patternnet' neural network in MATLAB R2014a using 5-fold cross validation. Where should i initialize weights of my neural network?

 *Position_1(for weight initialization)*

 for i=1:num_of_loops
 *Position_2(for weight initialization)* 

 - repeating cross validation
 for i=1:num_of_kfolds
 *Position_3(for weight initialization)*
 - Cross validation loop

 end
  end

I'm repeating 5-fold cross validation (because random selection of cross validation) to have more reliable outputs (average of neural network outputs). Which part is better for weight initialization (Position_1,Position_2 or Position_3) and why?

neural network , optimization , cross-validation , geh: good thread

Expert Answer

John Michell answered . 2024-11-14 21:22:58

To help understanding, I will assume Nval = Ntst = 0. Search for the nonzero examples in the NEWSGROUP and ANSWERS.

To design a typical I-H-O net with Ntrn training examples, try to not let the number of unknown weights

 Nw = (I+1)*H+(H+1)*O

exceed the number of training equations

 Ntrneq = Ntrn*O

This will occur as long as H <= Hub where Hub is the upperbound

 Hub = -1+ceil( (Ntrneq-O) / (I+O+1) )

Based on Ntrneq and Hub I decide on a set of numH candidate values for H

 0 <= Hmin:dH:Hmax <= Hmax

 numH = numel(Hmin:dH:Hmax)

and the number of weight initializations for each value of H, e.g.,

 Ntrials = 10

If the training target is ttrn = t(indtrn), the mean-square-error of a naïve constant output net (independent of the input) is

 MSEtrn00 = mean(var(ttrn',1));

Then using MSEtrn00 as a normalization reference, I use the following double loop format

 rng(0)
 j=0
 for h = Hmin:dH:Hmax
     j=j+1
     net = ...
     net.divideFcn = 'dividetrain';
          ... 
     for i = 1:Ntrials
         net = configure(net,x,t);
         ...
         [ net tr y e ] = train(net,x,t);
          ...
         R2(i,j) = 1-mse(e)/MSEtrn00;
      end
 end

For details, search for one of my designs using the search word greg and a subset of some the variables I always use ( e.g., Nw, Ntrneq, Hub, Ntrials ...)

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