How many degrees should be counted for computing the adjusted R^2 of a neural network?

Hi everyone,

I am trying to calculate the adusted R^2 of a network.Thus I should take into account the number of parameters of the network. The number of parameters delivered from a network with k inputs, i hidden units, 1 hidden layer kai n output should be equal to

k*l + l*n + bias hidden layer + bias in the output + k*n direct input-output connections.

Does anyone know if matlab has a bias in the output? Does anytone know if matlab calculates parameters for the direct input-output connections?

Thanks in advance

Answer 1

[Greg Heath]

Consider N pairs of I-dimensional "I" nput vectors and O-dimensional "O"utput target vectors. If Ntrn is the number of training pairs, the number of training equations is

 Ntrneq = Ntrn*O

If SSEtrn is the sum of squared training subset errors, corresponding mean-square-error, MSEtrn is given by

 MSEtrn = SSEtrn/Ntrneq

For an I-H-O feedforward net, the number of unknown weight variables to be estimated by the training subset pairs is

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

resulting in the number of training degrees-of-freedom

 Ntrndof = Ntrneq - Nw

Therefore, the DOF adjusted training set mean-square-error is given by

 MSEtrna = SSEtrn/ Ntrndof

I have posted zillions of examples in both the NEWSGROUP and ANSWERS. Some examples can be obtained with the search words

    greg MSEa

or

    greg MSEtrna

Hope this helps.

Thank you for formally accepting my answer

Greg