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How to calculate Akaike Information Criterion and BIC from a Neural Network?

Asked by Javier Bastante on 13 Feb 2017
Latest activity Answered by David Franco on 28 Aug 2017
I know "aic" function exists, but I don't know how to use it with fitting neural networks.
Any help?
Thank you in advance

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2 Answers

Answer by David Franco on 28 Aug 2017

After training the network and simulating the outputs:
[net,tr] = train(net,inputs,targets);
output = sim(net,inputs);
Get the parameters and calculate de criterions (Sarle, 1995):
% Getting the training targets
trainTargets = gmultiply(targets,tr.trainMask);
SSE = sse(net,trainTargets,output); % Sum of Squared Errors for the training set
n = length(tr.trainInd); % Number of training cases
p = length(getwb(net)); % Number of parameters (weights and biases)
% Schwarz's Bayesian criterion (or BIC) (Schwarz, 1978)
SBC = n * log(SSE/n) + p * log(n)
% Akaike's information criterion (Akaike, 1969)
AIC = n * log(SSE/n) + 2 * p
% Corrected AIC (Hurvich and Tsai, 1989)
AICc = n * log(SSE/n) + (n + p) / (1 - (p + 2) / n)
References:
  • Akaike, H. (1969), "Fitting Autoregressive Models for Prediction". Annals of the Institute of Statistical Mathematics, 21, 243-247.
  • Hurvich, C.M., and Tsai, C.L. (1989), "Regression and time-series model selection in small samples". Biometrika, 76, 297-307.
  • Sarle, W.S. (1995), "Stopped Training and Other Remedies for Overfitting". Proceedings of the 27th Symposium on the Interface of Computing Science and Statistics, 352-360.
  • Schwarz, G. (1978), "Estimating the Dimension of a Model". Annals of Statistics, 6, 461-464.

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Answer by Michelle Wu on 17 Feb 2017
Edited by Michelle Wu on 17 Feb 2017

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