5
$\begingroup$

I often use a ROC curve and the area under that curve as a measure of classifier accuracy in 2-class problems, e.g:

#Load a dataset
library(mlbench)
data(Sonar)

#Build a model
library(caret)
model <- train(Class~., data=Sonar, method='gbm', tuneLength=1, trControl=trainControl(method='cv'))
model

#ROC curve and AUC
library(pROC)
pMal <- predict(model, newdata=Sonar, type='prob')[,2]
roc(Sonar$Class, pMal, plot=TRUE)
>Area under the curve: 0.9705

#Lorez curve and gini?

enter image description here

In a similar manner, I would like to be able to plot the lorenz curve and calculate the gini coefficient for my classifier. I know Gini = 2*AUC-1, but I'm not actually sure how to calculate it on it's own. Furthermore, every application of a lorenz curve I've seen looks at univariate data (e.g. income distribution). How do I calculate a lorenz curve when I have 2 parameters: the predicted probability of the positive class, and the positive class itself?

$\endgroup$

1 Answer 1

3
$\begingroup$

Lorenz curve is also known under the name of "lift curve" when applied to classification/ranking. For a given range of predicted probability values, the lift represents a multiplicative increase in the positive class's rate (due to a given predictive model) over a random guess.

rocr package can calculate lift values/curves (the manual also has a concise definition of the lift). The Gini index can be calculated from the area under the lift curve (I typically use cumulative lift value at a given predicted probability threshold instead since it is easier to relate to business metrics)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.