My colleague and I uploaded a manuscript:
- Błaszczyszyn and Keeler, Determinantal thinning of point processes with network learning applications.
https://arxiv.org/abs/1810.08672
Details
The paper uses a (relatively) new model framework in machine learning. This framework is based on a special type of point process called a determinantal point process, which is also called a fermion point process. (This particle model draw inspiration from the form of the wave function in quantum mechanics.) Kulesza and Taskar introduced and developed the framework for using determinantal point processes for machine learning models.
The paper covers a type of generative machine learning (or Gen AI) model, due to its using randomness to create network outcomes. 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.
The training method for determinantal point processes is based on the maximum likelihood approach, which gives a convex optimization problem, allowing you to tackle it with your favourite gradient method, such as the BFGS or Adam method.
It turns out that point processes are amenable for looking at the signal-to-inference-plus-noise ratio (SINR) — see this post for details. More specifically, we found these point processes give tractable SINR-based expressions when you use (what I call) the standard (SINR) model, which I covered in a previous post.
Code
The MATLAB code for the producing the results in the paper can be found here:
https://github.com/hpaulkeeler/DetPoisson_MATLAB
I also re-wrote (or translated) the MATLAB code into Python:
https://github.com/hpaulkeeler/DetPoisson_Python
Further reading
My collaborators and I later extended this line of work in a separate paper, where we looked at the problem of designing a smart(er) medium access control (MAC) scheduling algorithm:
- Błaszczyszyn, Brochard, and Keeler, Coverage probability in wireless networks with determinantal scheduling.
https://arxiv.org/abs/2006.05038
I wrote about this work briefly in a later 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 recently uploaded:
- 2025 – Tu, Saha and Dhillon – Determinantal Learning for Subset Selection in Wireless Networks.
https://arxiv.org/abs/2503.03151