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guess right or wrong. There are indeed different kinds of wrong decisions
and different kinds of right decisions, and all of them have different costs
and benefits. And all these different costs and benefits can be explored to
design the right fitness function to evolve the right kind of model. For in-
stance, there is a difference between classifying correctly a malignant tumor
and classifying correctly a benign one.
More formally, there are four different possible outcomes of a single pre-
diction for a two-class problem with classes “1” (“yes”) and “0” (“no”). A
false positive FP is when the outcome is incorrectly classified as “yes” (or
“positive”), when it is in fact “no” (or “negative”). A false negative FN is
when the outcome is incorrectly classified as negative when it is in fact posi-
tive. True positives TP and true negatives TN are obviously correct classifi-
cations. In the first case, the outcome is correctly classified as positive; and,
in the latter, the outcome is correctly classified as negative.
Keeping track of all these possible outcomes is such an error-prone activ-
ity, that they are usually shown in what is appropriately called a confusion
matrix (Figure 3.9). Good results correspond to large numbers down the main
diagonal ( TP plus TN ) and to small numbers (ideally zero) off main diagonal
positions ( FP plus FN ).
These two kinds of error, false positives and false negatives, will gener-
ally have different costs. And obviously the two kinds of correct classifica-
tions, true positives and true negatives, will have different benefits. Thus,
for each problem, one can explore these differences between different costs
and benefits to evolve the right kind of model by using different kinds of
fitness functions. Let's take a look at some examples below.
Predicted Class
Ye s
N o
Yes
TP
FN
No
FP
TN
Figure 3.9. Confusion matrix for a two-class prediction.
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