Summary of Estimating Barycenters Of Distributions with Neural Optimal Transport, by Alexander Kolesov et al.
Estimating Barycenters of Distributions with Neural Optimal Transport
by Alexander Kolesov, Petr Mokrov, Igor Udovichenko, Milena Gazdieva, Gudmund Pammer, Evgeny Burnaev, Alexander Korotin
First submitted to arxiv on: 6 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 A novel approach to calculating the Wasserstein barycenter, an “average” distribution that aggregates reference distributions, is proposed. Building on the dual formulation of Optimal Transport (OT), a scalable method for solving this problem is developed, leveraging Neural OT solver with bi-level adversarial learning objective and general cost functions. This method outperforms traditional tri-level optimization-based approaches, which mainly focus on quadratic cost. Theoretical error bounds are established, and the methodology’s effectiveness is demonstrated in various scenarios and image data setups. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you have many different distributions that describe something similar, like how tall people are or what colors are popular. You want to find a single “average” distribution that combines all these smaller ones. This average is called the Wasserstein barycenter. A new way to calculate this average is developed by combining two existing methods: Optimal Transport and Neural OT solver. This method is faster and more flexible than previous approaches. The results show it works well in different situations, including analyzing images. |
Keywords
* Artificial intelligence * Optimization
