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I'm doing some ADA boosting with Decision stumps and in inducing a binary classifying decision stump, i'm finding both leaf nodes to have a positive value. Can this be the case? Is this possible?

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What is the overall response rate? If it's low (even 15-20%) it may be difficult to find decision stumps that contain one leaf with > 50% response!

You could consider oversampling or changing cutoff probability, but I think if your using only 2 leaf trees, your model is bound to struggle.

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