Add multitarget versions of the models

[ablaom]

By "multitarget" I mean vector-valued target y for regression.

In particular it would be good to have a multi-target version of elastic net regression, as I don't believe there is a pure julia version with an MLJ interface.

@tlienart Do you have a sense of how difficult this would be?

[tlienart]

I'd need to review the literature,I'm not sure but I think you can always reframe that as a standard scalar valued regression (I may be wrong) which would make this fairly straightforward

[tlienart]

Yeah so after a bit of research it looks like if you have a vector valued target y where each target has k dimensions then you can do:

[X 0; X 1; X 2; ... X k] (beta; gamma) = flatten(y)

so if you have a n x p feature matrix, a n x k target vector you end up with a standard regression problem with a stacked feature matrix of size (k x n) x (p+1) where the additional dimension is categorical.

I don't know how well this would work with the kind of model we have here where the assumption is that X is continuous. It might be that this is better handled by preprocessing and MLJLM just assumes you're giving it a standard (X, y) problem.

[ablaom]

Thanks @tlienart for looking into this. This looks completely generic. That is, we could apply this idea to any supervised model, not just the linear ones in this package. Do I understand correctly?

[tlienart]

I think that's right yes, I don't have experience with it though. I believe it's linked to an approach called "hard parameter sharing". An alternative that discards dependency between target dimensions is to just fit several linear models in parallel but that's a bit sad (multioutputregressor).