Scalable unbalanced optimal transport using generative adversarial networks
Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We for...
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| Format: | Article |
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2021
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| Online Access: | https://hdl.handle.net/1721.1/130122 |
| _version_ | 1826216776664350720 |
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| author | Yang, Karren Dai Uhler, Caroline |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Yang, Karren Dai Uhler, Caroline |
| author_sort | Yang, Karren Dai |
| collection | MIT |
| description | Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. We provide theoretical justification for this formulation, showing that it is closely related to an existing static formulation by Liero et al. (2018). We then propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practice to GANs, and perform numerical experiments demonstrating how this methodology can be applied to population modeling. |
| first_indexed | 2024-09-23T16:52:56Z |
| format | Article |
| id | mit-1721.1/130122 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:52:56Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1301222022-10-03T08:54:48Z Scalable unbalanced optimal transport using generative adversarial networks Yang, Karren Dai Uhler, Caroline Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. We provide theoretical justification for this formulation, showing that it is closely related to an existing static formulation by Liero et al. (2018). We then propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practice to GANs, and perform numerical experiments demonstrating how this methodology can be applied to population modeling. 2021-03-11T21:14:01Z 2021-03-11T21:14:01Z 2019-05 2019-05 Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/130122 Yang, Karren D. and Caroline Uhler. "Scalable unbalanced optimal transport using generative adversarial networks." 7th International Conference on Learning Representations, May 2019, New Orleans, Louisiana. https://openreview.net/forum?id=HyexAiA5Fm 7th International Conference on Learning Representations Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Prof. Uhler via Phoebe Ayers |
| spellingShingle | Yang, Karren Dai Uhler, Caroline Scalable unbalanced optimal transport using generative adversarial networks |
| title | Scalable unbalanced optimal transport using generative adversarial networks |
| title_full | Scalable unbalanced optimal transport using generative adversarial networks |
| title_fullStr | Scalable unbalanced optimal transport using generative adversarial networks |
| title_full_unstemmed | Scalable unbalanced optimal transport using generative adversarial networks |
| title_short | Scalable unbalanced optimal transport using generative adversarial networks |
| title_sort | scalable unbalanced optimal transport using generative adversarial networks |
| url | https://hdl.handle.net/1721.1/130122 |
| work_keys_str_mv | AT yangkarrendai scalableunbalancedoptimaltransportusinggenerativeadversarialnetworks AT uhlercaroline scalableunbalancedoptimaltransportusinggenerativeadversarialnetworks |