Gaussian Process Model with Turing

[kevbonham]

Thanks! This is super useful. I suppose no surprise it looks similar to the AbstractGPs solution posted on zulip.

@willtebbutt

Given that additive models appear to be on the table, do you believe that a model of the form

f(x, t) = f_t(t) + f_x(x)

is plausible for your data? (where x is all variables other than time). If so we could modify the above example to express that structure.

Yes, I think that’s plausible, where I think we’d likely assume f_x() would have a linear covariance function.

@willtebbutt

As regards @luiarthur’s proposal to 1-hot encode your “subject” variable – I wouldn’t have though that should be necessary as the length scale associated with that dimension can just be made really small, so that the value for each subject can be more-or-less independent from the other (if indeed the fact that they look like they’re ordinal is just a coincidence and there’s really no reason to think 1 and 2 are more closely related than 1 and 5)

That is definitely the assumption for the majority of our problems. There actually are some cases where subjects are part of the same household, and then we might hypothesize some connection, but we’d encode that in a separate “household” variable. Subject IDs themselves could just as well be random Strings, they’re strictly identifiers and have no meaning.