My collaborators and I uploaded a manuscript:
- Błaszczyszyn, Brochard, and Keeler, Coverage probability in wireless networks with determinantal scheduling.
https://arxiv.org/abs/2006.05038
Details
The paper builds off some previous work by us that uses a (relatively) new model in machine learning:
- Błaszczyszyn and Keeler, Determinantal thinning of point processes with network learning applications.
https://arxiv.org/abs/1810.08672
The new machine learning model is based on a special type of point process called a determinantal point process. It was originally called a Fermion point process. These are useful point processes as the exhibit certain closure properties under certain operations such independent thinning.
Determinantal point processes are random objects and, when they are properly trained or fitted, can serve as generative artificial intelligence (or Gen AI) models. In fact, you can interpret these point processes as a special Gibbsian point processes, which have at their core a Hamiltonian function. A Hamiltonian is generalized type of energy function, which is also the basis for other generative (or stochastic) models such as Boltzmann machines.
Kulesza and Taskar introduced and developed the framework for using determinantal point processes for machine learning models.
Code
The MATLAB code for the producing the results in the paper can be found here:
https://github.com/hpaulkeeler/detcov_matlab
I also re-wrote the MATLAB code into Python:
https://github.com/hpaulkeeler/detcov_python
Further reading
Our work started with this related paper:
- Błaszczyszyn and Keeler, Determinantal thinning of point processes with network learning applications.
I wrote about this work briefly in an earlier post.
Parallel (or orthogonal, perhaps) to our work, is this paper:
- 2019 – Saha and Dhillon – Machine Learning meets Stochastic Geometry: Determinantal Subset Selection for Wireless Networks.
https://arxiv.org/abs/1905.00504
Update: A manuscript extending the above line of research by Saha and Dhillon was uploaded:
- 2025 – Tu, Saha and Dhillon – Determinantal Learning for Subset Selection in Wireless Networks.
https://arxiv.org/abs/2503.03151