The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
Authors: Thibault Sejourne, Francois-Xavier Vialard, Gabriel Peyré
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, we provide numerical experiments on synthetic examples and domain adaptation data with a Positive-Unlabeled learning task to highlight the salient features of the unbalanced divergence and its potential applications in ML. |
| Researcher Affiliation | Academia | Thibault Séjourné Ecole Normale Supérieure, DMA, PSL thibault.sejourne@ens.fr François-Xavier Vialard Université Gustave Eiffel francois-xavier.vialard@u-pem.fr Gabriel Peyré Ecole Normale Supérieure, DMA, CNRS, PSL gabriel.peyre@ens.fr |
| Pseudocode | Yes | Algorithm 1 UGW(X, Y, ρ, ε) Input: mm-spaces (X, Y), relax. ρ, regul. ε Output: π, γ solving (6) |
| Open Source Code | Yes | All implementations are available at https: //github.com/thibsej/unbalanced_gromov_wasserstein, and installable in Python with the command pip install unbalancedgw. |
| Open Datasets | Yes | We consider PU learning over the Caltech office dataset used for domain adaptation tasks (with domains Caltech (C) Griffin et al. [2007], Amazon (A), Webcam (W) and DSLR (D) Saenko et al. [2010]). |
| Dataset Splits | Yes | We report the accuracy of the prediction over the same 20 folds of the datasets, and use 20 other folds to validate the parameters of UGW. ... The value (ρ1, ρ2) {2 k, k J5, 10K}2 are cross validated for each task on the validation folds, and we report the average accuracy on the testing folds. |
| Hardware Specification | No | The paper mentions that the algorithm is “GPU-friendly” but does not provide any specific hardware details such as GPU models, CPU types, or memory specifications. |
| Software Dependencies | No | The paper mentions 'installable in Python with the command pip install unbalancedgw' and refers to the 'unbalanced Sinkhorn algorithm', but does not specify Python version, or any other software dependencies with version numbers (e.g., specific deep learning frameworks or numerical libraries). |
| Experiment Setup | Yes | We set ε = 2 9, which avoids introducing an extra parameter in the method. The value (ρ1, ρ2) {2 k, k J5, 10K}2 are cross validated for each task on the validation folds, and we report the average accuracy on the testing folds. We consider 100 random samples for each fold of (X, Y ), a ratio of positive samples r = 0.1 for domains (C,A,W,D), and a ratio r = 0.2 for domains (C,A,W). |