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The structure of this table looks similar to the cost matrix that was
illustrated in Figure 7-2, but the confusion matrix cells have the model's
incorrect and correct prediction counts. If we consider Attriter as the
positive target value, false-positive ( FP ) prediction count is 60, and the
false-negative ( FN ) prediction count is 30.
Although the confusion matrix measures misclassification of target
values, in our example, false-negatives are three times costlier than
the false-positives. To assess model quality from a business perspec-
tive, we need to measure cost in addition to accuracy. The total cost
of false predictions is 3
150. If with a different model
you get 40 false-positives and 40 false-negatives, then the overall
accuracy is better, however total cost is more at 3
160. If
a cost matrix is specified, it is important to consider cost values to mea-
sure the performance and select the model with the least cost value.
Receiver operating characteristics ( ROC ) is another way to compare
classification model quality. An ROC graph places the false positive
rate on the X-axis and true positive rate on the Y-axis as shown in
Figure 7-7. Here, the false positive rate is the ratio of the number of
false positives and the total number of actual negatives. Similarly, the
true positive rate is the ratio of the number of true positives and the
total number of actual positives.
To plot the ROC graph, the test task determines the false positive
and true positive rates at different probability thresholds . Here, the
probability threshold is the level above which a probability of the
predicted positive target value is considered a positive prediction.
Different probability threshold values result in different false positive
rates and true positive rates. For example, when the Attriter predic-
tion probability is 0.4 and the probability threshold is set to 0.3, the
customer is predicted as an Attriter . Whereas if the probability
threshold is 0.5, the customer is predicted as a Non-attriter as
illustrated in Figure 7-7(a).
Figure 7-7(b) illustrates the ROC curves of two classification models
that are plotted at different probability thresholds. These models per-
form better at different false positive rates; for example, at a false
positive rate of 0.1, Model B has better true positives than Model A.
However, at 0.3 and above the false positive rate of Model A outper-
formed that of Model B. Based on the accepted false positive rate,
users can select the model and its probability threshold. The area
under the ROC curve is another measure of overall performance of a
classification model. The higher the area under the ROC curve, gen-
erally, the better the model performance.
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