(a) Probability threshold
False Positive Rate
(b) ROC curves
Receiver operating characteristics.
In the ROC graph, the point (0,1) is the perfect classifier 4 : it classifies
all positive cases and negative cases correctly. It is (0,1) because the
false positive rate is 0 (none), and the true positive rate is 1 (all). The
point (0,0) represents a classifier that predicts all cases to be negative,
while the point (1,1) corresponds to a classifier that predicts every
case to be positive. Point (1,0) is the classifier that is incorrect for all
Lift and cumulative gain are also popular metrics to assess the
effectiveness of a classification model. Lift is the ratio between the
results obtained using the classification model and a random selec-
tion. Cumulative gain is the percentage of positive responses deter-
mined by the model across quantiles of the data. Cases are typically
divided into 10 or 100 quantiles against which the lift and cumula-
tive gain is reported, as illustrated later in Table 7.5. The lift chart
and cumulative gains charts are often used as visual aids for assess-
ing model performance. An understanding of how cumulative lift
and cumulative gains are computed helps in understanding the
cumulative lift and cumulative gains charts illustrated in Figure 7-8.
A classification model is also referred to as a classifier since it classifies cases
among the possible target values.