Projection Robust Wasserstein Distance and Riemannian Optimization
Authors: Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, Michael Jordan
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide comprehensive empirical studies to evaluate our algorithms on synthetic and real datasets. Experimental results confirm our conjecture that the PRW distance performs better than its convex relaxation counterpart, the SRW distance. Moreover, we show that the RGAS and RAGAS algorithms are faster than the Frank-Wolfe algorithm while the RAGAS algorithm is more robust than the RGAS algorithm. |
| Researcher Affiliation | Collaboration | Tianyi Lin Chenyou Fan Nhat Ho Marco Cuturi , Michael I. Jordan University of California, Berkeley The Chinese University of Hong Kong, Shenzhen University of Texas, Austin CREST ENSAE , Google Brain {darren_lin,jordan}@cs.berkeley.edu, fanchenyou@cuhk.edu.cn, minhnhat@utexas.edu cuturi@google.com |
| Pseudocode | Yes | Algorithm 1 Riemannian Gradient Ascent with Sinkhorn Iteration (RGAS), Algorithm 2 Riemannian Adaptive Gradient Ascent with Sinkhorn Iteration (RAGAS) |
| Open Source Code | No | The paper provides links to third-party software used (e.g., POT software package and the SRW implementation by Paty and Cuturi), but it does not include a statement or link for the open-sourcing of their own developed methodology (RGAS, RAGAS) code. |
| Open Datasets | Yes | Additional results on MNIST dataset are deferred to Appendix H. |
| Dataset Splits | No | The paper mentions running experiments 'over 100 samples' and varying 'number of points n' for synthetic data and using 'empirical distributions' and 'real data' (movie scripts, Shakespeare plays, MNIST), but it does not specify explicit training, validation, or test dataset splits with percentages, sample counts, or clear methodologies for data partitioning. |
| Hardware Specification | No | The paper mentions 'Comparisons of mean computation times on CPU' but does not provide any specific details about the CPU model, number of cores, memory, or any other hardware components used for running the experiments. No GPU information is provided either. |
| Software Dependencies | No | The paper mentions 'POT software package3 [34]', 'Frank-Wolfe algorithm2 [69]', and 'WORD2VEC [62]' as tools used or baselines, but it does not specify version numbers for any of these software dependencies. |
| Experiment Setup | Yes | For the RGAS and RAGAS algorithms, we set γ = 0.01 unless stated otherwise, β = 0.8 and α = 10 6. The details of our full setup can be found in Appendix G. ... threshold ϵ = 0.001. ... regularization parameter is set as η = 0.2 for n < 250 and η = 0.5 otherwise4, as well as the scaling for the matrix C (cf. Definition 2.4) is applied for stabilizing the algorithms. |