@Cambridge_Uni Grad - Astrophysics | @join_EF alumni | a tired MedTech founder and entrepreneur | hoping to take a break and do PhD in applying 
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We wrote about the "what, when, and why?" of t-processes: http://proceedings.mlr.press/v33/shah14.pdf . Implementation isn't much more difficult. There are nuanced trade-offs. The uncertainty and dependencies are subtly different and sometimes preferable, the noise model is less interpretable. https://twitter.com/GarridoMerchan/status/1342899907989032961 …
Which situations do you think a t-process would be preferable over GP with Bayesian treatment of scale?
We address the question in depth in the paper. It's actually quite subtle and hard to give a short take. They're mostly useful when you have a small number of observations (e.g. BayesOpt with a really expensive objective). But there is more to the story.
In 5.1.1 you discuss the LL and MSE for TP vs GP. The results on spatial and wine data were particularly noteworthy; with the TP having lower MSE scores and ridiculously high LL scores. I wasn't sure why this was the case.
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