Linear optimal partial transport embedding
Authors: Yikun Bai, Ivan Vladimir Medri, Rocio Diaz Martin, Rana Shahroz, Soheil Kolouri
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test the approximation performance of OPT using LOPT. Given K empirical measures {µi}K i=1, for each pair (µi, µj), we compute OPTλ(µi, µj) and LOPTµ0,λ(µi, µj) and the mean or median of all pairs (µi, µj) of relative error defined as |OPTλ(µi, µj) LOPTµ0,λ(µi, µj)| / OPTλ(µi, µj) . For our experiments, we created K point sets of size N = 500 for K different Gaussian distributions in R2. |
| Researcher Affiliation | Academia | 1Department of Computer Science, Vanderbilt University, 366 Featheringill, Nashville, TN 37240, USA 2Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA. |
| Pseudocode | No | The paper provides mathematical formulations and descriptions of methods but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code is available at https://github.com/ Baio0/Linear OPT. |
| Open Datasets | Yes | Point Cloud Interpolation: We test OT geodesic, LOT geodesic, HK geodesic, LHK geodesic, OPT interpolation, and LOPT interpolation on the point cloud MNIST dataset. ... PCA analysis: We compare the results of performing PCA on the embedding space of LOT, LHK and LOPT for point cloud MNIST. We take 900 digits from the dataset corresponding to digits 0, 1 and 3 in equal proportions. |
| Dataset Splits | No | The paper mentions using the MNIST dataset but does not specify the exact training, validation, and test splits (e.g., percentages or sample counts) used for the experiments. |
| Hardware Specification | Yes | The experiment was conducted on a Linux computer with AMD EPYC 7702P CPU with 64 cores and 256GB DDR4 RAM. ... The experiments are conducted on a Linux computer with AMD EPYC 7702P CPU with 64 cores and 256GB DDR4 RAM. |
| Software Dependencies | No | The paper mentions "Python OT" as the LP solver used but does not specify its version number or any other software dependencies with version details. |
| Experiment Setup | Yes | For our experiments, we created K point sets of size N = 500 for K different Gaussian distributions in R2. In particular, µi N(mi, I), where mi is randomly selected such that mi = 3 for i = 1, ..., K. For the reference, we picked an N point representation of µ0 N(m, I) with m = P mi/K. ... In OPT and LOPT interpolation, we set λ = 20; in HK and LHK, we set the scaling to be 2.5. ... We test for η = 0, 0.5, 0.75 (see Figure 8 in the Appendix H). |