Gini vs AUC

KadsuraKadsura
edited May 2024 in GLM.Validation

"This is different to the Gini index for two reasons.

  1. The Gini index is measuring the area between the Lorenz curve and the line of equality, whereas here we are measuring the area under the ROC and ignoring the line of equality for this calculation.
  2. The Gini index requires multiplication by 2 and AUROC doesn't.

However, you can calculate one from the other."

I think there may be more than 2 differences? Gini is from the Lorenz curve where the AUC is from the ROC graph. The source footnote says, "Specifically, the AUROC is equal to 0.5 × normalized Gini + 0.5, where normalized Gini is the ratio of the model’s Gini index to the Gini index of the hypothetical “perfect” model (where each record’s prediction equals its actual value). "

I didn't exactly understand this statement, so googled the topic. This paper states for Gini = 2*AUC -1 to work there needs to be a couple of more assumptions,

AUC_Metron May 2019 v4.pdf (weizmann.ac.il)

Comments

  • adminadmin

    Thanks for pointing this out. While the CAS does have a history of asking questions based on footnotes I think you're okay here with knowing the Gini index isn't equal to the AUROC.

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