Warmlab

What is a WARM?

A WA-reinfrocement model (WARMs) is an interesting stochastic process inspired by the development of human brain [1]. Consider a graph $G$ with vertices $V$ and edges $E$. Initially we start with some counts $N^{(0)}_e$ (typically $N^{(0)}_e=1$) for all the edges $e\in E$. At each time step $t$, we select a vertex $v$ and reinforce an edge $e$ incident to $v$ randomly using their counts as weights, i.e., the probability of selecting $e$ is $$\frac{N^{(t)}e}{\sum{f\text{ incident to }v} N^{(t)}_f},.$$

After the reinforcement, $N^{(t+1)}_e = N^{(t)}_e + 1$ for the chosen $e$ and the counts for other edges remain the same. Interested readers can have a look at [1] for more details on the model and its interesting properties.

This package implements useful utilities for studying WA-reinforcement models, written as a part of my MSc thesis project in mathematics and statistics.

Usage

Building from Source and Installation

Clone the project and navigate to the root directory. To install the package, build the project using

python -m build .

It should be fairly quick and this generates a dist folder. Locate warm-vx.x.x.tar.gz under that folder where the version is the current version and run

pip install -r requirements.txt
pip install dist/warm-vx.x.x.tar.gz

to complete the installtion, after which you can import it as any other Python package.

A few examples are under notebooks, which should run when the above steps are compeleted.

High-performance Computing Deployment

Doc to be written.

Developing the Package

Clone the project to your local directory. In order to avoid dependency clashes when working with the project, it is highly recommended to setup a virtual environment with

virtualenv warmlab

and install the dependencies only

pip install -r requirements.txt

Notice that we are not builidng the package nor installing the package itself, because we do not want older code to mess with the newer code in the environment. To run the code under a development environment, use module-level run commands under the project root, e.g.

python -m warmlab.warm

References

[1] Remco van der Hofstad et al. “Strongly reinforced Pólya urns with graph-based competition”. In: The Annals of Applied Probability 26.4 (2016), pp. 2494–2539.