Summary of Low-rank Optimal Transport Through Factor Relaxation with Latent Coupling, by Peter Halmos et al.
Low-Rank Optimal Transport through Factor Relaxation with Latent Coupling
by Peter Halmos, Xinhao Liu, Julian Gold, Benjamin J Raphael
First submitted to arxiv on: 15 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
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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 The paper presents an alternative parameterization of the low-rank optimal transport (OT) problem based on the latent coupling (LC) factorization. The LC factorization is a generalization of previous work by [Forrow et al. 2019] and [Lin et al. 2021]. This new framework has several advantages, including decoupling the problem into three OT problems, greater flexibility, and improved interpretability. A new algorithm, Factor Relaxation with Latent Coupling (FRLC), is derived using coordinate mirror descent to compute the LC factorization. FRLC can handle multiple OT objectives and marginal constraints while maintaining linear space complexity. The paper demonstrates the effectiveness of FRLC on various applications, including graph clustering and spatial transcriptomics. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper shows how to solve a big problem in machine learning using a clever new way to break it down into smaller problems. This makes it easier to do and understand. It’s like solving a puzzle! The new method is called Factor Relaxation with Latent Coupling (FRLC). FRLC can be used for many different things, like grouping similar things together or comparing how things are connected. |
Keywords
» Artificial intelligence » Clustering » Generalization » Machine learning
