On Robust Optimal Transport: Computational Complexity and Barycenter Computation
Authors: Khang Le, Huy Nguyen, Quang M Nguyen, Tung Pham, Hung Bui, Nhat Ho
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we provide numerical evidences regarding our presented complexities for ROBUST-SEMISINKHORN and ROBUST-IBP algorithms. We put additional experiments (including the runtime comparison of ROT/RSOT on synthetic and real datasets, as well as some applications for the studied robust formulations) in Appendix F. |
| Researcher Affiliation | Collaboration | University of Texas, Austin (...) Vin AI Research (...) Massachusetts Institute of Technology |
| Pseudocode | Yes | Algorithm 1: ROBUST-SEMISINKHORN (...) Algorithm 2: ROBUSTIBP |
| Open Source Code | Yes | Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] |
| Open Datasets | Yes | We also carry out a similar experiment on MNIST data, which is reported in the Appendix F. |
| Dataset Splits | No | For RSOT, we let n = 100, τ = 1, generate entries of C uniformly from the interval [1, 50] and draw entries a, b uniformly from [0.1, 1] then normalizing them to form probability vectors. η is set according to Theorem 1. For each ε varying from 5 10 2 to 5 10 5, we calculate the number of theoretical and empirical iterations described above, as well as their ratio. This experiment is run 10 times and we report their mean and standard deviation values in Figure 3 (a). We also carry out a similar experiment on MNIST data, which is reported in the Appendix F. No explicit splits (train/val/test) are described for MNIST or the synthetic data in the main text. |
| Hardware Specification | Yes | All the experiments are conducted on a server with 32 GB RAM, 8 cores Intel(R) Core(TM) i7-9700K and 1 Ge Force RTX 2080 GPU. |
| Software Dependencies | No | All the optimal solutions for convex problems in the following part are computed using the cvxpy library [1]. No version number is provided for cvxpy or any other software dependencies. |
| Experiment Setup | Yes | For RSOT, we let n = 100, τ = 1, generate entries of C uniformly from the interval [1, 50] and draw entries a, b uniformly from [0.1, 1] then normalizing them to form probability vectors. η is set according to Theorem 1. For each ε varying from 5 10 2 to 5 10 5, we calculate the number of theoretical and empirical iterations described above, as well as their ratio. (...) For RSBP, we run the ROBUSTIBP algorithm with the following setup: n = 10; τ = 1; p1, . . . , pm, [ω1, . . . , ωm] are randomly-initialized probability vectors; {Ci}m i=1 is a set of n n matrices whose entries drawn uniformly in [0.01, 0.1]; five chosen values of ε vary from 10 3 to 10 5 (...); and the corresponding values of η are set according to Theorem 2. |