On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Error
Authors: Quang Minh Nguyen, Hoang H. Nguyen, Yi Zhou, Lam M. Nguyen
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Extensive experiments on synthetic and real datasets validate our theories and demonstrate the favorable performance of our methods in practice. We showcase GEM-UOT on the task of color transfer in terms of both the quality of the transfer image and the sparsity of the transportation plan. |
| Researcher Affiliation | Collaboration | Quang Minh Nguyen EMAIL Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge, MA, USA Hoang H. Nguyen EMAIL Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA, USA Yi Zhou EMAIL IBM Research Almaden Research Center San Jose, CA, USA Lam M. Nguyen Lam EMAIL IBM Research Thomas J. Watson Research Center Yorktown Heights, NY, USA |
| Pseudocode | Yes | Algorithm 1 GEM-UOT Algorithm 2 GEM-RUOT Algorithm 3 GEM-OT Algorithm 4 PROJ |
| Open Source Code | No | The paper does not contain any explicit statement about providing source code for the methodology described, nor does it provide a link to a code repository. The license mentioned pertains to the paper itself, not the accompanying code. |
| Open Datasets | Yes | To practically validate our algorithms, we compare the GEM-UOT with Sinkhorn on CIFAR10 dataset (Krizhevsky and Hinton, 2009). A pair of flattened images corresponds to the marginals a, b, whereby the cost matrix C is the matrix of ℓ1 distances between pixel locations. This is also the setting considered in (Pham et al., 2020; Dvurechensky et al., 2018). We plot the results in Figure 4, which demonstrates GEM-UOT superior performance. Additional experiments on Fashion-MNIST dataset that further cover GEM-RUOT are presented in Appendix D. |
| Dataset Splits | No | The paper mentions using CIFAR-10 and Fashion-MNIST datasets and creating marginals from image pairs, but it does not specify any training, validation, or test dataset splits for model development or evaluation, which would be crucial for reproduction. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the experiments, such as GPU or CPU models, memory, or cloud computing specifications. |
| Software Dependencies | No | The paper mentions using "the convex programming package cvxpy to find the exact UOT plan (Agrawal et al., 2018)" but does not specify a version number for cvxpy or any other software dependencies. |
| Experiment Setup | Yes | We set n = 200, τ = 55, α = 4, β = 5. Then ai s are drawn from uniform distribution and rescaled to ensure α = 4, while bi s are drawn from normal distribution with σ = 0.1. Entries of C are drawn uniformly from [10 1, 1]. For both GEM-UOT and Sinkhorn, we vary ε = 1 10 4 to evaluate their time complexities in Figure 1 and test the τ dependency in Figure 2. Unless specified otherwise, we always set η = ε 2R = 2ε (α+β)2 (according to Theorem 13). |