Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2010.11970 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913289893576704 |
|---|---|
| author | Wang, Jie Gao, Rui Xie, Yao |
| author_facet | Wang, Jie Gao, Rui Xie, Yao |
| contents | We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize the theoretical property of the finite-sample convergence rate on IPMs and present practical algorithms for computing this metric. Numerical examples validate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_11970 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Two-sample Test using Projected Wasserstein Distance Wang, Jie Gao, Rui Xie, Yao Machine Learning We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize the theoretical property of the finite-sample convergence rate on IPMs and present practical algorithms for computing this metric. Numerical examples validate our theoretical results. |
| title | Two-sample Test using Projected Wasserstein Distance |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2010.11970 |