Conference
The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
| العنوان: | The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation |
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| المؤلفون: | Séjourné, Thibault, Vialard, François-Xavier, Peyré, Gabriel |
| المساهمون: | Laboratoire d'Informatique Gaspard-Monge (LIGM), École nationale des ponts et chaussées (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel |
| المصدر: | NeurIPS ; https://hal.science/hal-04435914 ; NeurIPS, 2021, Virtual conference, France. ⟨10.48550/arXiv.2009.04266⟩ |
| بيانات النشر: | CCSD arXiv |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Optimization and Control (math.OC), Machine Learning (stat.ML), FOS: Mathematics, FOS: Computer and information sciences, [MATH]Mathematics [math] |
| جغرافية الموضوع: | Virtual conference, France |
| Time: | Virtual conference, France |
| الوصف: | International audience ; Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW) distance, which is the solution of a quadratic assignment problem. The GW distance is however limited to the comparison of metric measure spaces endowed with a probability distribution. To alleviate this issue, we introduce two Unbalanced Gromov-Wasserstein formulations: a distance and a more tractable upper-bounding relaxation.They both allow the comparison of metric spaces equipped with arbitrary positive measures up to isometries. The first formulation is a positive and definite divergence based on a relaxation of the mass conservation constraint using a novel type of quadratically-homogeneous divergence. This divergence works hand in hand with the entropic regularization approach which is popular to solve large scale optimal transport problems. We show that the underlying non-convex optimization problem can be efficiently tackled using a highly parallelizable and GPU-friendly iterative scheme. The second formulation is a distance between mm-spaces up to isometries based on a conic lifting. Lastly, we provide numerical experiments onsynthetic 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. |
| نوع الوثيقة: | conference object |
| اللغة: | English |
| DOI: | 10.48550/arXiv.2009.04266 |
| الاتاحة: | https://hal.science/hal-04435914 https://doi.org/10.48550/arXiv.2009.04266 |
| رقم الانضمام: | edsbas.9C096FF0 |
| قاعدة البيانات: | BASE |
| DOI: | 10.48550/arXiv.2009.04266 |
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