I am trying to implement the approximate GP method you use in brms. I have it working, but I do not understand how you are making predictions.
I know with exact GPs, you need old and new data, and you need to compute the kernel using multiple covariance matrices. I perused your code, and see exactly what I expect for exact GPs.
But for approximate GPs, you say you only need the old data. Where does the ‘new’ data come in?? Obviously, it works - I can just use predict(brmsFit, newDS), and newDS only has one value in it, and it can predict using the approximate GP. Where in your code do you actually use the supplied data, and compute a predicted value? I see .predictor_gpa, but I don’t understand how we get from old-data to new-data predictions.