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The textbook tells us that we should choose an attribute with the maximum information gain to split a decision tree. My question is what if all information gains are zero? Should we stop splitting or we split the tree with all attributes?

An example of this question is $Y=a~XOR~b$. To determine the value of $Y$, the information gains of $a$ and $b$ are zero. How do we build a decision tree for this question?

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  • $\begingroup$ If the information gain is zero, there's no further purpose of splitting unless a combination of features yields information. I'm looking into that very question now: stats.stackexchange.com/questions/259176/… $\endgroup$
    – Brian Bien
    Commented Jan 31, 2017 at 17:25

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