Summary of A Riemannian Approach to Ground Metric Learning For Optimal Transport, by Pratik Jawanpuria et al.
A Riemannian Approach to Ground Metric Learning for Optimal Transport
by Pratik Jawanpuria, Dai Shi, Bamdev Mishra, Junbin Gao
First submitted to arxiv on: 16 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper proposes a novel approach to optimal transport (OT) theory, which has gained popularity in machine learning and signal processing applications. The authors introduce a method to learn a suitable latent ground metric for OT-based distances by parameterizing it with a symmetric positive definite matrix. By leveraging the rich Riemannian geometry of these matrices, the learned metric is jointly optimized with the OT distance. The paper demonstrates the effectiveness of this approach in OT-based domain adaptation tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research explores how to improve optimal transport theory for machine learning and signal processing. The key idea is to learn a special kind of map that helps compare different datasets. To do this, the authors use a mathematical structure called symmetric positive definite matrices. This allows them to find the best possible match between datasets while also considering their underlying relationships. The results show that this new approach can help with adapting data from one domain to another. |
Keywords
» Artificial intelligence » Domain adaptation » Machine learning » Signal processing
