I'm learning about trees in my data science class recently and I know that the convention is to use regression trees when the response is continuous and classification trees when the response is categorical.

However, let's say we have a dataset with a binary response, is there any justification to still use a regression tree over a classification tree? Moreover, are there real-world instances where a regression tree performs classification better than a traditional classification tree?

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    $\begingroup$ They aren't fundamentally different things. A binomial GLM is both clearly a regression model and a classifier. $\endgroup$ – Frans Rodenburg Apr 11 '19 at 2:27

It is not simply convention. You are using trees, if the response is continuos, then they are called regression trees, and if the response is categorical, then they are called classification trees. But they are still trees, and perform in the same way.

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