Low-Rank Optimal Transport through Factor Relaxation with Latent Coupling
Authors: Peter Halmos, Xinhao Liu, Julian Gold, Benjamin Raphael
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We compare FRLC to existing low-rank and full-rank optimal transport algorithms on several datasets: simulated datasets previously used in Tong et al. (2023) and Scetbon et al. (2021); a massive spatialtranscriptomics dataset Chen et al. (2022); and a graph partitioning task Chowdhury & Needham (2021). |
| Researcher Affiliation | Academia | Peter Halmos1,*, Xinhao Liu1,*, Julian Gold2,*, and Benjamin J. Raphael1 1Department of Computer Science, Princeton University 2Center for Statistics and Machine Learning, Princeton University |
| Pseudocode | Yes | Algorithm 1 Balanced FRLC (Section 3.3), Algorithm 4 FRLC (General marginal constraint low-rank optimal transport) (Section C), and Algorithm 6 Initialize-Couplings (Section F). |
| Open Source Code | Yes | We will upload all code, and all code required to generate the synthetic data experiments used. |
| Open Datasets | Yes | We compare FRLC to existing low-rank and full-rank optimal transport algorithms on several datasets: simulated datasets previously used in Tong et al. (2023) and Scetbon et al. (2021); a massive spatialtranscriptomics dataset Chen et al. (2022); and a graph partitioning task Chowdhury & Needham (2021). |
| Dataset Splits | Yes | We pick the best hyperparameters using the Spearman correlation on the gene expression prediction task for 10 validation genes: Ckb, Fabp7, Myl4, Tnnt2, Apoa2, Hba-x, Tubb3, Epha7, Ldha, Col1a2, which are marker genes of various cell types as well. |
| Hardware Specification | No | FRLC has half the runtime of LOT (CPU) (Table 2 caption) and This experiment, and the experiments on mouse embryo spatial transcriptomics, were conducted on cluster GPUs. (Section L.4). No specific CPU/GPU models or detailed hardware specifications were provided. |
| Software Dependencies | No | We initialize LOT using the rank-2 initialization and two other options in ott-jax Cuturi et al. (2022). (Section 4.1) and We preprocess the dataset using the standard SCANPY Wolf et al. (2018) pipeline. (Section M.2). No specific version numbers are provided for these software dependencies. |
| Experiment Setup | Yes | We perform extensive grid search to find the best hyperparameter combinations for each method and each problem. The grid of hyperparameters searched for each method is reported in Table. 6. The best performing hyperparameter combination for each method is reported in Table. 7 along with the performance on the validation genes. (Section M.3) and FRLC sets τ = 75 and γ = 90, with a maximum of 200 iterations and a minimum of 25 iterations, subject to the stopping criterion given in (10). (Section N.3) |