MATLAB: Multiple Nonlinear Regression Equation using Neural Network Toolbox

Question

I am analysing data with six inputs and one output. I had trained a network using Neural Network Toolbox. I want this network to predict the mathematical model or a regression equation. For instance I have six inputs as x1, x2, x3, x4, x5, x6 and one output y. I had trained a network which gives me R=0.999 which seems very good.

Now I want that network provide me an equation in the form.

y= a1*x1^b1 + a2*x2^b2 + a3*x3^b3 + a4*x4^b4 + a5*x5^b5+ a6*x6^b6

How I can get the constants a's and b's.

Regards and thanks in advance.

Answer 1

R = 0.999 doesn't mean much unless you can convince us that you did not over-train an over-fit net:

size(x) = [ I N ] % I = 6, N = ?

size(t) = [ O N ] % O =1, N = ?

How was the data divided? Ntrn, Nval, Ntst = ?

Did you use TRAINBR, TRAINLM or TRAINSCG?

Number of training equations Ntrneq = Ntrn*O = ?

How many nodes in the hidden layer? H = ?

Number of unknown weights and biases Nw = {I+1)*H+(H+1)*O = O + (I+O+1)*H = ?

Number of estimation degrees of freedom = Nw - Ntrneq = ?

What are the normalized mean-square errors for the train, val and test subsets? For example,

ttrn = t(trainInd), etc

NMSEtrn = mse(ttrn -ytrn) / var(ttrn,1)

R2trn = 1 - NMSEtrn

Rtrn = sqrt(R2trn)

is Rtst = 0.999?

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A neural net is trained on known input/target examples. I do not see any way you can estimate the as and bs with a neural net.

Hope this helps.

Thank you for formally accepting my answer

Greg