Is there an example implementing sparse approximation for gaussian processes in STAN? I would learn about this since it might be helpful when we have lots of data.
It depends on what you mean by sparse approximation of GP.
- Basis function approximations are also low rank approximations and there is code available for a basis function approach discussed in Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming.
- Another common family of approaches is inducing point based approaches. I’m not aware of code for such for Stan and there is a reason to suspect that they would be slow in the current Stan. The reason is that inducing point sparse approximations rely on lot of matrix-matrix and matrix-vector operations, and the way the current Stan handles autodiff for matrices is not optimal for that. There is work in progress that will make Stan autodiff much faster in case of matrices that are transformations of data and a small number of covariance function parameters, which is the typical case for sparse and non-sparse GPs.