README.md

Sparse-UOT

Code for our ICML '24 paper, Submodular Framework for Structured-Sparse Optimal Transport, Poster.

To install the 'sparse_ot' package, please clone this repository & run pip install .. The list of packages specific to the experiments has been shared separately in their respective folders (under examples/).

Notations:

• $\gamma$: Optimal Transport plan
• $K$: Cardinality constraint.

Implementation of Algorithms

1. GenSparse UOT, general sparsity constraint:
   • Implementation when $K$ unspecified.
   • Implementation when $K$ specified.

Note

While our experiments use a sparse vectorial representation of $\gamma$, we also provide implementation with $\gamma$ as a matrix: (i) code when $K$ unspecified, (ii) code when $K$ specified.

2. ColSparse UOT, column-wise sparsity constraint: Implementation.

Tip

'ws' in the function names signifies warm start, where we use the previous outer iteration's $\gamma$. We found that a warm start results in faster optimization.

Toy example with Gaussians:

• GenSparse UOT Supplementary.
• CS-UOT.

Codes for the experiments are under 'examples/'.

If you find this useful, consider giving a ⭐ to this repository and citing our work.