Conference
On the complexity of the optimal transport problem with graph-structured cost
| Title: | On the complexity of the optimal transport problem with graph-structured cost |
|---|---|
| Authors: | Fan, Jiaojiao, Haasler, Isabel, Karlsson, Johan, Chen, Yongxin |
| Publisher Information: | KTH, Matematik (Inst.) KTH, Optimeringslära och systemteori Georgia Tech, Atlanta, GA 30332 USA PMLR |
| Publication Year: | 2022 |
| Collection: | Royal Inst. of Technology, Stockholm (KTH): Publication Database DiVA |
| Subject Terms: | Computational Mathematics, Beräkningsmatematik |
| Description: | Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for addressing new challenges in the field of machine learning. However, the usage of MOT has been largely impeded by its computational complexity which scales exponentially in the number of marginals. Fortunately, in many applications, such as barycenter or interpolation problems, the cost function adheres to structures, which has recently been exploited for developing efficient computational methods. In this work we derive computational bounds for these methods. In particular, with $m$ marginal distributions supported on $n$ points, we provide a $ \mathcal\tilde O(d(\mathcalT)m n^w(G)+1ε^-2)$ bound for a ε-accuracy when the problem is associated with a graph that can be factored as a junction tree with diameter $d(\mathcalT)$ and tree-width $w(G)$. For the special case of the Wasserstein barycenter problem, which corresponds to a star-shaped tree, our bound is in alignment with the existing complexity bound for it. ; QC 20220511 |
| Document Type: | conference object |
| File Description: | application/pdf |
| Language: | English |
| Relation: | Proceedings of Machine Learning Research; Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, p. 9147-9165; orcid:0000-0002-2484-0181; orcid:0000-0001-5158-9255; http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-312088; ISI:000841852303024 |
| Availability: | http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-312088 |
| Rights: | info:eu-repo/semantics/openAccess |
| Accession Number: | edsbas.F6B27EB8 |
| Database: | BASE |
| Description not available. |