Questions / Quant research, Machine learning judgment
An interaction hides from a greedy first split
For the XOR data, what is the weighted Gini impurity after either one-feature root split?
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Answer: 0.5 Gini impurity (1/2)
- Each child gets one positive and one negative.
- Each child’s Gini is 0.5.
- The weighted average is 0.5: no decrease.
Interview shortcut. Balanced children: Gini stays 0.5.
Takeaway. Greedy splits can see zero gain on interactions.
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