Gini Index and Friends

35 Pages Posted: 19 Oct 2022

See all articles by Christian Lorentzen

Christian Lorentzen

Schweizerische Mobiliar Versicherungsgesellschaft

Michael Mayer

Schweizerische Mobiliar Versicherungsgesellschaft

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: October 14, 2022

Abstract

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.

Keywords: Gini index, Gini score, Gini coefficient, accuracy ratio, consistency, consistent scoring, auto-calibration, Lorenz curve, concentration curve, cumulative accuracy profile, CAP, receiver operating characteristics curve, ROC curve, area under the curve, AUC, model selection, binary classification

JEL Classification: G22, C45, C18

Suggested Citation

Lorentzen, Christian and Mayer, Michael and Wuthrich, Mario V., Gini Index and Friends (October 14, 2022). Available at SSRN: https://ssrn.com/abstract=4248143 or http://dx.doi.org/10.2139/ssrn.4248143

Christian Lorentzen

Schweizerische Mobiliar Versicherungsgesellschaft ( email )

Michael Mayer

Schweizerische Mobiliar Versicherungsgesellschaft ( email )

Mario V. Wuthrich (Contact Author)

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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