README.md

Collisional Optimal Transport

In this repository, we present an implementation of collision-based dynamics for the optimal transport problem. This git repository has been used to produce results in the following paper:

Sadr, Mohsen, and Hossein Gorji. "Collision-based Dynamics for Multi-Marginal Optimal Transport." arXiv preprint at arXiv:2412.16385 (2024).

Numpy Implementation

Here, we provide the most accessible (and not fastest) implementation of the collisional OT in NumPy. Simply, first import the library

from collision_numpy import collOT_numpy

Given the samples are stored in X with shape (number of marginals, number of samples, dimension of each sample) the optimal pairing with the minimum $L2$ cost between marginals can be found via

X, log_loss, nt = collOT_numpy(X)

C Implementation

For faster runs on the CPU, we have prepared an implementation in C with a Python wrapper. To use it, first, you need to compile the code. On Linux, it can be done on a terminal simply by

cd src/
python3 setup.py build_ext --inplace

Then, in the Python code, import the collOT_c via

from collision_wrapper import collOT_c

and call the function via something like

X, log_loss, nsteps = collOT_c(X, MinIter=100, MaxIter=1000, tol = 1e-6, avg_window=20, Track=1)

PyTorch Implementation

We provide a PyTorch implementation of the collision-based dynamics to solve the 2-marginal optimal transport problem to be used as a loss function in training statistical models. First, import the function via

from collision import collOT_pytorch

and then call it simply by

x, y, log_loss = collOT_pytorch(x, y)

Here, x and y contain samples of each marginal with shape (number of samples, dimension of each sample).

For examples of how this implementation can be used, see the Jupyter Notebooks in examples/ directory.