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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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