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

I know "aic" function exists, but I don't know how to use it with fitting neural networks.

Any help?

Thank you in advance

Answer 1

[David Franco]

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.

Answer 2

[Michelle Wu]

Please check out a similar MATLAB Answers post attached below:

http://www.mathworks.com/matlabcentral/answers/195674-neural-network-aic-and-bic-calculation-number-of-parameters