A Higher Precision Algorithm for Computing the $1$-Wasserstein Distance
Authors: Pankaj K Agarwal, Sharath Raghvendra, Pouyan Shirzadian, Rachita Sowle
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 EXPERIMENTS In this section, we conduct experiments to show that our algorithms from Section 3 and Section 4 improve the accuracy of the additive approximation algorithms. We test an implementation of our algorithm, written in Python, on discrete probability distributions derived from real-world and synthetic data sets. All tests are executed on a computer with a 2.50 GHz Intel Core i7 processor and 8GB of RAM using a single computation thread. ... As shown in Figure 2 (a) (d), our algorithm runs significantly faster than both the Sinkhorn and the LMR algorithms while producing solutions of similar quality. |
| Researcher Affiliation | Academia | Pankaj K. Agarwal1*, Sharath Raghvendra2, Pouyan Shirzadian2, and Rachita Sowle2 1Duke University, 2Virginia Tech |
| Pseudocode | No | The paper describes the algorithm steps in prose but does not provide a formal pseudocode block or algorithm box. |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for their methodology is openly available. |
| Open Datasets | Yes | For a real-world dataset, we use the Adult Census Data (UCI repository), which is a point cloud in R6 with continuous features for 35, 000 individuals, divided into two categories by income (Dua & Graff (2017)). |
| Dataset Splits | No | The paper mentions datasets but does not provide specific details on how the datasets were split into training, validation, or test sets. |
| Hardware Specification | Yes | All tests are executed on a computer with a 2.50 GHz Intel Core i7 processor and 8GB of RAM using a single computation thread. |
| Software Dependencies | No | The paper mentions "Python" and refers to "Sinkhorn method (Cuturi (2013))" and "LMR algorithm (Lahn et al. (2019))" as black-boxes, but no specific version numbers for these software components or any other libraries are provided. |
| Experiment Setup | No | While the paper states, "We set the parameters of the Sinkhorn and LMR algorithms in such a way that the error produced by them matches with the error produced by our 1-Wasserstein algorithm," this is a high-level goal for setting parameters of other algorithms, not a detailed description of the experimental setup (e.g., learning rates, batch sizes, epochs) for their proposed methods. |