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On the Qualitative Behavior of Impurity-Based Split t;ing Rules I: The Minima-Free Property

Purdue University
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We show that all strictly convex n impurity measures lead to splits at boundary points, and furthermore show that certain rational splitting rules, notably the information gain ratio, also have this property. A slightly weaker result is shown to hold for impurity measures that are only convex n, such as Inaccuracy.

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