A determinantally-thinned (Poisson) point process is essentially a discrete determinantal point process whose underlying state space is a single realization of a (Poisson) point process defined on some (bounded) continuous space. I believe this is a new type of point process, originally proposed in the paper by Blaszczyszyn and Keeler[1]:
https://arxiv.org/abs/1810.08672
An obvious question is whether a determinantally-thinned Poisson point process is also a determinantal point process? The answer, we believe, is no, but it's far from obvious.
Run the file DemoDetPoisson.m for a demonstration of simulating/sampling a determinantally-thinned Poisson point process.
Most of the remaining MATLAB files were used to obtain the results in the paper by Blaszczyszyn and Keeler[1]. In particular, they create and fit determinantally-thinned Poisson point process to dependently-thinned Poisson point processes such as Matern hard-core point processes; for details see[1]. The fitting (or supervised learning) method is based on that developed by Kulesza and Taskar[2].
To reproduce the results in the paper by Blaszczyszyn and Keeler[1], first run SubsetGenerate.m, then SubsetDetPoissonFit.m, and finally SubsetDetPoissonGenerate.m. The first two files will create .mat files (stored locally), which contain variable values (that is, simulation/sampling and fitting results).
To reproduce the exact same results in the paper[1], set the random seed to one in the files SubsetGenerate.m and SubsetDetPoissonGenerate.m. That is, in these two files remove the comment from the line that reads:
%seedRand=1; rng(seedRand)
See comments in the individual MATLAB .m files for more information.
I also wrote some of this code (for example DemoDetPoisson.m and TestDetPoisson.m) in R, Python and Julia, which have a very similar structure; see
https://github.com/hpaulkeeler/DetPoisson_Julia
https://github.com/hpaulkeeler/DetPoisson_Python
https://github.com/hpaulkeeler/DetPoisson_R
For a very brief introduction on these point processes, see my post on simulating them:
https://hpaulkeeler.com/simulating-matern-hard-core-point-processes/
For more information, I recommend the references at the end of the post.
H.P. Keeler, Inria/ENS, Paris, and University of Melbourne, Melbourne, 2018.
[1] Blaszczyszyn and Keeler, Determinantal thinning of point processes with network learning applications, 2018.
https://arxiv.org/abs/1810.08672
[2] Kulesza and Taskar, "Determinantal point processes for machine learning",Now Publisers, 2012