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I have been doing research using Support Vector Regression for some time, especially using radial basis kernel, for predicting a response variable from a set of numeric predictors. As a consequence of this work, I wrote an article with my results and submitted it to a journal.

Now, one reviewer is asking me to justify if my SVR model with radial basis kernel is modelling somehow interactions between predictors...

I know that polynomial kernels include interactions explicitly. I also know that radial basis kernel does not. However, radial basis functions are considered a universal approximator and in this other question (https://stats.stackexchange.com/a/491484/233634) a user (Firebug) stated that any universal approximator can implicitly model interactions between predictors (he/she uses an example based on a neural network).

I am not a mathematician and I confess that I am a bit far from truly understanding the properties of universal approximators.

Is the radial basis function really able to model interactions between predictors implicitly? How could I check/prove wether my model is doing it?

Thanks ;)

P.S.: There is an old question about a very similar topic (SVM, variable interaction and training data fit), but, even given the great answer by Dikran Marsupial, the specific matter about radial basis and interactions remains unclear, in my opinion.

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  • $\begingroup$ While I can't comment on how to check whether your model is modeling interactions, if you look at the expansion of the radial basis kernel as shown in its Wikipedia article, you can see it includes $(x^Tx')^j$, which means interaction is involved, just as with polynomial kernel. $\endgroup$
    – syockit
    Commented Nov 22, 2023 at 10:15

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