I want to use a method to select a diverse subset of a bulky set, to which the Determinantal Point Process is a solution. However, based on my basic knowledge of DPP, the first step is making a matrix of $N*N$ (the Gram matrix), in which $N$ is the main set size. As $N$ for my problem is about $10^6$.
I want to know that is there any version of DPP that can tractably sample from a set with that size? Is it possible to not calculate the Gram matrix explicitly?
It would be great to introduce resources that can fit into my context.
Thanks