What are the advantages of curve fitting to regression Neural Network ?

It just came as a curiosity

are there situations that curve fitting might be better?

I know that these 2 toolboxes are comparable only in case of 1 input 1 output

Answer 1

[Star Strider]

Curve Fitting —

• Advantages: If you know the mathematical model of the process that produced your data, you can (likely) estimate the parameters of the process with reasonable accuracy, giving you insight into the process. It is a parametric regression.
• Disadvantages: You have to have a reasonably representative model of your system to start with, and a reasonably accurate initial estimate of your parameter set (at least with respect to orders-of-magnitude) in order to get a reasonable fit.

Neural Nets —

• Advantages: You do not need to have a model of your system for the net to provide a reasonable approximation of your data.
• Disadvantages: Since it is a non-parametric ‘black box’, you learn nothing about the dynamics of your system.

I have used both, and where appropriate, neural nets can be robust for many kinds of problems. However, since I almost always want to know the parameters of the process I am modeling, I usually use parametric methods now.

[farzad]

Thanks a lot Star

[Star Strider]

My pleasure!

Answer 2

[Greg Heath]

Since NNs like FITNET do both, I think you are confused w.r.t. terminology.

Do you mean when to use the neural toolbox instead of the statistics (or another) toolbox?

It depends on the difficulty of the problem and how you want to analyze the result.

Don't forget that although FITNET with a single hidden layer is a universal approximator,

the NNET Toolbox doesn't have any statistical testing algorithms. Therefore, you could use

the NNET for the fit and another toolbox for the analysis.

[farzad]

thank you very much Dear Professor