Calculating probability of draw from posterior distribution

[andersdot]

I'm fitting a GP to some data y1, and want to calculate the probability of some different data, y2, under that GP model.

So p( y2 | GP(y1) )

Is that possible?

Cheers

[Balandat]

Yeah you can compute the posterior prediction under your input x2 if associated with a pair (x2, y2) - for an exact GP this will give you a MVN, and you can then just compute the log prob of the data y2 under that.

[andersdot]

Thanks! If I'm not doing an exact GP, how do I calculate the log prob of data y2?

[gpleiss]

It should be the same for a variational model. Train the variational model on x1, y1, and then make a prediction on x2. This should also output an MVN, and so you could then compute the logprob of y1.

Of course, everything is approximate in this case.