Introduction to JuliaGPs + Turing #423
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| Unfortunately, there is not a simple way to enforce monotonicity in the samples from a GP, | ||
| and we can see this in some of the plots above, so we must hope that we have enough data to | ||
| ensure that this relationship approximately holds under the posterior. | ||
| In any case, you can judge for yourself whether you think this is the most useful | ||
| visualisation that we can perform -- if you think there is something better to look at, | ||
| please let us know! |
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Maybe this is crazy (and I'm def not suggesting we put this in the tutorial), but could we perform a quick linear regression and use this as a prior for the GP?
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Hmmmm I'm not entirely sure that I understand. If I've understood correctly, the suggestion is to look at the data in order to inform our prior, which I'm not sure makes sense to me.
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So this would indeed make it, I dunno, "semi-Bayesian" or something, but it could be a useful trick to get monotonicity (though it wouldn't guarantee it). But I guess the proper way would be to just treat it as a multivariate normal and model the mean directly?
Another thing, is it sensible to put a prior on the GP prior?
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Well in some ways we are here -- we're placing a prior over the kernel parameters, which is implicitely placing a prior over the GP prior. Are you imagining something non-parametric though?
I've written up the tutorial I made for the BSU workshop into a TuringTutorial. I think it's okay to go as-is, but I suspect that people will have ideas on how it could be improved, so I'd like to iterate a bit before merging.
I would appreciate the following two kinds of feedback: