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Consider binary classification problem and popular quality measure ROC AUC (which is almost the same as Gini coefficient G = 2*AUC - 1 ).

Assume we have two features F1, F2.

Question (rough version) :

Can we bound Gini/AUC of the model built using both F1 and F2 by individual Gini/AUC of F1 and F2 ?

It seems more accurate formulation of the question should additionally impose requirement on the class of the models beeing considered. Since Gini/AUC is invariant under monotonic transformation it seems natural to consider the "models" M(f1,f2) which are monotonic functions of f1,f2. For example logistic regression models.

It seems natural that Gini of such model would be bounded by sum of Gini. Probably correlation may allow to sharpen that bound.

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