Gini Index and Friends

In the machine learning community, the Gini index is a very popular score for model selection, and it is also used in actuarial science for evaluating insurance pricing models. The purpose of this tutorial is to discuss the Gini index, both its version in economics and its version in machine learning, which differ. We discuss its relationship to the area under the curve (AUC) of the receiver operating characteristics (ROC) curve, which is often used for model selection in binary classification problems. A main deficiency of the Gini index is that it does not give us a consistent scoring function. Therefore, simply maximizing the Gini index may lead to wrong decisions. The issue is that the Gini index is a rank-based score that is not calibration-sensitive. However, if we use the Gini index for scoring within the class of auto-calibrated regression models, it gives us a strictly consistent scoring function and, henceforth, a sensible model selection tool. This will be discussed in this tutorial