Name
Abstract | ||
|---|---|---|
Optimal Transport (OT) has become a powerful tool to compare probability distributions. However, it suffers from a severe computational burden for high dimensional and continuous distributions. To this end, we develop two novel methods for the Kantorovich and Monge formulations, which are the fundamental problems in OT. First, we learn the optimal joint distribution in the Kantorovich formulation and propose an algorithm, namely Cop-OT, which transforms the primal objective of the Kantorovich problem into a tractable objective with respect to the copula parameter. Second, based on the copula formulation of the joint distribution, we learn the optimal map in the Monge problem and propose an algorithm, namely Map-OT, which describes the optimal map using a parameterized function estimated by approximating the barycentric projection of the optimal joint distribution and then obtains a tractable objective with respect to parameters of interest. Both of them can be solved by stochastic optimization with a stable optimizing process. Empirical results demonstrate that Cop-OT and Map-OT can gain more accurate approximations of the Kantorovich and Monge problems compared with the baseline methods. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1002/int.22795 | INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS |
Keywords | DocType | Volume |
copula, optimal map, optimal plan, optimal transport | Journal | 37 |
Issue | ISSN | Citations |
8 | 0884-8173 | 0 |
PageRank | References | Authors |
0.34 | 0 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jinjin Chi | 1 | 0 | 0.34 |
| Bilin Wang | 2 | 0 | 0.34 |
| Huiling Chen | 3 | 0 | 0.34 |
| Lejun Zhang | 4 | 78 | 15.62 |
| Ximing Li | 5 | 44 | 13.97 |
| Jihong OuYang | 6 | 94 | 15.66 |