# What is a sparse Gaussian process?

In the paper Junction Tree Variational Autoencoder for Molecular Graph Generation, section 3.2, the authors state that they train a sparse Gaussian process to predict a chemical property, $$y(m)$$, of a molecule $$m$$, given the latent representation of the molecule (which is represented by the mean of the variational or hidden distribution).

A Gaussian processes is a collection of infinitely many random variables such that every linear combination of a finite-length subset of those random variables is normally distributed.

What is a sparse Gaussian process? How is it trained? In a supervised way? How does the dataset look like? What do we use a SGP for?

• The key bottleneck in gaussian processes(GPs) is the inversion of the kernel matrix with complexity $O(n^3)$. Sparse GPs overcome that by using few inducing points($m$) that cover the data space of $n$ points effectively. This can lead to $O(nm^2)$ inference complexity. Here are some references gpss.cc/gpss15/talks/talk_james.pdf, prowler.io/blog/… – randomprime May 15 at 21:22