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From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: Fitting Criterias, are there any more of them?
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Date: Wed, 15 Feb 1995 22:22:28 GMT
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In article <NSANDHU.95Feb10075504@grizzly.water.ca.gov>, nsandhu@venice.water.ca.gov (Nicky Sandhu) writes:
|>      I have been using NN's for six months now. I have been
|> observing that SSE is the only criteria used for fitting during
|> calibration. ( Feed-forward networks used).

There are many other training criteria that can be used. Choice of
the appropriate criterion depends on knowledge of the distribution
of the noise. Maximum likelihood is a very general approach to
constructing training criteria. See, for example:

   Cramer, J. S. (1986) Econometric Applications of Maximum Likelihood
   Methods, Cambridge University Press: Cambridge.

   McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models,
   2nd ed., Chapman & Hall: London.

|>      Now I am faced with another problem. The criteria used to
|> judge the fit is based on the percentage error at each data point with
|> respect to the output data point's magnitude.
|>      i.e. %error = 100* (Target - Model output)/ Target
|>
|>      Is it possible to use this criteria to train the neural network.

Sure, if you square it. Since the target values are known, that is
simply weighted least squares.

|> I have taken the log of the output and this improves performance with
|> respect to the percentage error criteria.

Taking logs is indeed an approximation to the above criterion if the
errors are small.

|> I have a feeling the NN
|> would do much better if trained with the same criteria as it is being
|> judged by.

Quite so.

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
