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I am testing out different models for a regression task. When using OLS, Ridge and Lasso, I use different polynomial degrees of the explanatory variables. Example: For two variables x and y, degree 2 would give the explanatory variables x, x^2, xy, y, y^2.

When using decision tree, however, I am not sure whether it makes sense to use any any higher degrees than 1 as explanatory variables. Example: Does it make sense to test for x^2, xy and y^2 when applying a decision tree regressor?

The reason I ask, is that the decision tree regressor is a non-linear regressor. On the one hand this could perhaps be an arguement it not making sense to include higher order polynomials, as the decisoin tree already can deal with non-linearity.

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Since CARTs (Classification And Regression Tree) are a non-parametric algorithm, they should be able to find interactions between variables and non-linear behaviors.

Nevertheless, building polynomials can help them have a better performance.

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  • $\begingroup$ Thanks for answering. I'll apply higher degree polynomials also for the decision tree regressor. $\endgroup$
    – KJA
    Jan 21, 2020 at 6:51

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