Modeling with Neural Networks: Principles and Model Design Methodology - Neural Networks: Methodology and Applications - page 102

Fig. 2.4. Cumulative distribution function of the probe feature

having both true variables: the second variable happens to be, by chance, just
as relevant as one of the true variables.

Example 3

In a classification problem, a data base was generated, containing 200 ex-
amples with 1,326 candidate variables, including 52 independent variables,
among which 2 relevant variables were present. With a 1% risk, the probe
feature method selected both relevant variables, and no other.
Once the inputs are selected, they can be used as inputs to a neural net-
work.
That method is directly related to Fisher's test, which is discussed in the
additional material at the end of the chapter.

2.4.2.4 Relation Between Fisher's Test and the Probe Feature
Method

The interested reader will find in [Stoppiglia 1998; Stoppiglia et al. 2003] the
proof of the following result: if the model under consideration at iteration k of
the Gram-Schmidt orthogonalization procedure is complete, i.e., if it contains
all relevant variables, and if it is true, i.e., if the regression function belongs
to the family of functions within which the model is sought, then the selection
procedure performed at iteration k is equivalent to a Fisher's test between the
models examined at iterations k and k 1.

Therefore, the probe feature method has two advantages on Fisher's test:
first, it gives a clear and intuitive interpretation to the selection criterion;
second, it is applicable whether the complete model is available or not, and
whether the model is true or not.

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