Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization
Authors: Kaheon Kim, Rentian Yao, Changbo Zhu, Xiaohui Chen
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., 1024 1024 images) 2D synthetic and real data. ... Using both synthetic and real data, we compare our approach with two existing methods applicable to distributions supported on large grids. |
| Researcher Affiliation | Academia | 1Department of ACMS, University of Notre Dame, IN, USA. 2Department of Mathematics, University of British Columbia, BC, Canada. 3Department of Mathematics, University of Southern California, CA, USA. Correspondence to: Changbo Zhu <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 H1-Gradient Ascent Algorithm ... Algorithm 2 Gradient Descent-Ascent Algorithm on Euclidean Domain ... Algorithm 3 Wasserstein-Descent H1-Ascent Algorithm ... Algorithm 4 Wasserstein-Descent H1-Ascent Algorithm ... Algorithm 5 L2-Descent H1-Ascent Algorithm |
| Open Source Code | No | The paper does not provide an explicit statement about releasing its own source code or a link to a code repository for the methodology described. It only mentions using the third-party library POT: Python Optimal Transport (Flamary et al., 2021) and Py Proximal. |
| Open Datasets | Yes | Here, our method is applied to the high-resolution handwritten digits data (Beaulac & Rosenthal, 2022). |
| Dataset Splits | No | The paper describes using synthetic uniform distributions and one hundred handwritten images of the digit 8 for experiments, but it does not specify any training/test/validation dataset splits. The task is barycenter computation on given distributions, which does not typically involve such splits. |
| Hardware Specification | Yes | All methods were executed on Google Colab with an L4 GPU. |
| Software Dependencies | No | The paper mentions using the Python library POT: Python Optimal Transport (Flamary et al., 2021) and the Python function pyproximal.Simplex in the library Py Proximal. However, specific version numbers for these software dependencies are not provided. |
| Experiment Setup | Yes | For this simulation, we apply Algorithm 4 and set τt = exp( t/T) and η1 i = 0.05 for all i and decrease it by a factor of 0.99 if Iµi νt (φt+1 i ) < Iµi νt (φt i). ... To run Algorithm 4, we set τt = exp( t/T), and η1 i = 0.5 at iteration t = 1 and decrease it by a factor of 0.95 whenever Iµi νt (φt+1 i ) < Iµi νt (φt i). The barycenters computed by our method, CWB, and DSB using T = 300 iterations are displayed in the bottom row of Figure 2. |