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Positive Predictive Value / Negative Predictive Value
The positive predictive value / negative predictive value fitness function is
based both on the positive predictive value (PPV) and negative predictive
value (NPV) indicators. Both these indicators are also commonly used in
medicine, with the PPV reflecting the percentage of people with a positive
diagnostic test result who actually have the disease, and the NPV reflecting
the percentage of people with a negative diagnostic test who do not have the
disease.
More formally, the positive predictive value PPV i of an individual pro-
gram i is evaluated by the equation:
TP
PPV
i
,
where
TP
FP
z
0
(3.15)
i
i
i
TP
FP
i
i
and the negative predictive value NPV i is evaluated by:
TN
i
NPV
,
where
TN
FN
z
0
(3.16)
i
i
i
TN
FN
i
i
And again, by multiplying both these indicators and using this new index
as basis to measure the fitness of the evolved models, one forces the discov-
ery of models that have both high PPV and NPV. Thus, the PPV/NPV PN i of
an individual program i is evaluated by the equation:
PN
PPV
NPV
(3.17)
i
i
i
And for evaluating the fitness f i of an individual program i , the following
equation is used:
f
1000
PN
(3.18)
i
i
which obviously ranges from 0 to 1000, with 1000 corresponding to the ideal.
And now that we know how to measure the fitness of different kinds of
evolving programs, let's see how they are selected to reproduce.
3.2.4 Selection Mechanism
In gene expression programming, individuals are selected according to fitness
by roulette-wheel sampling (see, for instance, Goldberg 1989). This means
that each individual receives a slice of the roulette-wheel proportional to its
 
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