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

38 vues (au cours des 30 derniers jours)
I know "aic" function exists, but I don't know how to use it with fitting neural networks.
Any help?
Thank you in advance

Réponse acceptée

David Franco
David Franco le 28 Août 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.

Plus de réponses (1)

Michelle Wu
Michelle Wu le 17 Fév 2017
Modifié(e) : Michelle Wu le 17 Fév 2017

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