Different kernels for KCI implementation

[nataliaglazman]

Hi, I am using FCI with KCI testing for my dataset. I have some one-hot encoded variables and some continuous variables. As far as I know, using a Gaussian kernel for testing between categorical and continuous variables is not recommended. Would it be useful to write an implementation of different kernels specifically for categorical variables and maybe even enable selection of different kernel combinations for one dataset?

[kunwuz]

Yes, this sounds very interesting and practical! At the same time, I'm not fully sure whether any issue exists. Did you find any reference supporting that type of 'hybrid' kernel?

[nataliaglazman]

I have had this idea for a while, but couldn't find much referencing it. Today I came across this paper which essentially sets the width of the RBF kernel to be very small to approximate the Dirac kernel (a kernel for categorical variables) in the cases of categorical variables. I still need to read up on the implementation and proofs but could be interesting to look into! I think in practice RBF kernels do ok with categorical data but there is definitely room for improvement as far as I can tell from literature.