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From what I've read you should you use group lasso to either discard the dummy encoded variables (of the category) or use all of them. If you use normal lasso then some of the variables in the group can be discarded (set to zero) and some might not, but why is this an issue?

Let's say we have a categorical variable with 3 levels (A, B, C) and we dummy encode it to get columns A, B (C when A=B=0). Now if we, with normal lasso, only keep A, shouldn't the interpretation then be that when A=1 we get A and when it is 0 we get either B or C, where it doesn't matter that much which one (B or c) it is. What am I missing?

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  • $\begingroup$ Have you read that this should be done or just that it might be desirable? Wikipedia reads more like the latter. $\endgroup$ – Ben Reiniger Jul 15 '19 at 14:22
  • $\begingroup$ @BenReiniger You're right it seems like they say it's desirable, like here they use "usually". But from a predictive standpoint group lasso seems undesirable. $\endgroup$ – Ferus Jul 15 '19 at 19:16

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