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Jan 10, 2021 at 19:22 comment added Ben Reiniger @Freguglia, that's not a problem here, because the "groups variances" refers to the dependent variable, not the features. All a decision tree cares about is the relative ordering of features, so (assuming $x$ is positive), $x^{200}$ carries the same information as $x$ for a tree model.
Sep 8, 2018 at 21:58 comment added VFreguglia I don't agree with this answer. Decision trees are built based on groups variances and if your transformation is not linear, then, in the other scale, the "most heterogeneous" grouping can change. As an example, a feature is uniformly distributed on (0,0.1) for a group and on (0.95,1.05) for the other, now take the non-linear transformation x^200 and there is a high chance those guys between 0.95 and 1.00 will be classified with the first group .
Jan 12, 2017 at 2:25 comment added Firebug If your variable allows negative values squaring is not a monotonic transformation, and the forest will therefore pick that.
Dec 15, 2015 at 22:44 comment added whuber A little more care in this analysis would be welcome, because squaring is not a one-to-one transformation. Thus a comparison of the square to a threshold is not quite the same thing as a comparison of the original variable to a threshold. This issue can be fixed up, provided the transformation is sufficiently nice, but what about the case of multivariate transformations of variables, such as $x_1x_2$? That's no mere "rescaling."
Sep 21, 2015 at 16:33 vote accept Dean MacGregor
Apr 22, 2013 at 23:03 history answered sashkello CC BY-SA 3.0