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2.4.2.5 What to do in Practice?
Summary of the procedure for discarding irrelevant variables:
1. Choose the set of candidate inputs (primary and secondary variables).
2. Select the input that is most correlated to the output; in observation
space, project all other inputs, and the output, onto the null subspace of
the selected input.
3. In the null space of the m
1 variables selected at previous iterations
(a) Select the projected input vector that is most correlated to the pro-
jected output vector.
(b) Compute the probability H m for the probe feature to be more relevant
than one of the m input selected previously, and compare it to the risk
α chosen by the designer.
(c) If H m is smaller than the risk, project the projected output, and
all remaining candidate inputs, onto the null space of the selected
projected input and iterate to step 3.
(d) If H m is larger than the risk, proceed to step 4.
4. Use the selected variables as inputs of a neural network and train as
indicated in the next sections.
2.4.3 Conclusion on Variable Selection
The first step in any model design procedure consists in reducing the dimen-
sion of the input space, by asking two questions.
Is the intrinsic dimension of the input vector as small as possible, or is it
possible to find a more compact input representation, while preserving the
amount of relevant information?
Are all candidate inputs relevant to the modeling of the quantity of
interest?
The answer to the first question is provided by principle component analy-
sis, or possibly by more complex operations such as curvilinear component
analysis or self-organizing maps.
The answer to the second question is provided by statistical methods such
as the probe feature method.
After performing input selection, the parameters of the model are esti-
mated as discussed in the next section.
2.5 Estimation of the Parameters (Training) of a Static
Model
We now turn to the problem of estimating the parameter of a model g ( x , w ):
find the numerical values of the components of the parameter vector w that
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