Neural Optimal Transport with General Cost Functionals
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916265347514368 |
|---|---|
| author | Asadulaev, Arip Korotin, Alexander Egiazarian, Vage Mokrov, Petr Burnaev, Evgeny |
| author_facet | Asadulaev, Arip Korotin, Alexander Egiazarian, Vage Mokrov, Petr Burnaev, Evgeny |
| contents | We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_15403 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Neural Optimal Transport with General Cost Functionals Asadulaev, Arip Korotin, Alexander Egiazarian, Vage Mokrov, Petr Burnaev, Evgeny Machine Learning We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure. |
| title | Neural Optimal Transport with General Cost Functionals |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2205.15403 |