Efficient Gaussian Process | The Birthday problem

[Niko]

Hey,

thank you for your interest! I’d guess that if you really want/need to do full MCMC, then you won’t get around optimizing your model in the way that I did and adaptively tuning the approximation and the parametrization.

However there are two important caveats: First, currently you can’t do what I did because none of the publicly available Stan interfaces supports it. Second, and depending on the problem more importantly, you might not need to do full MCMC.

I have very little experience with GPs, but your problem sounds as if this discussion could be very helpful to you: Gaussian process regression

I’m sure @avehtari could tell you more, but I’d guess the following quote applies for your problem as well:

@avehtari

If you want to model all interactions, have binomial observation model, 5000 observations and 14 variables, use something else than Stan.

If you are happy with an additive model, have binomial observation model, 5000 observations and 14 variables, you can try the basis function approximated GP also in Stan (probably good to use glm compound functions for speedup).

For comparison, the Birthday problem has ~7300 observations and a single dimension, both in input and output.