Summary of Distributional Matrix Completion Via Nearest Neighbors in the Wasserstein Space, by Jacob Feitelberg et al.
Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space
by Jacob Feitelberg, Kyuseong Choi, Anish Agarwal, Raaz Dwivedi
First submitted to arxiv on: 17 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Methodology (stat.ME)
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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 introduces a new problem called distributional matrix completion, which aims to impute true distributions associated with both observed and unobserved matrix entries. To solve this issue, the authors leverage optimal transport tools to generalize the nearest neighbors method for the distributional setting. Under a suitable latent factor model on probability distributions, they establish that their method recovers distributions in the Wasserstein norm. The paper demonstrates the effectiveness of their approach through simulations, showcasing its ability to provide better distributional estimates and accurate calculations of standard deviation and value-at-risk. Additionally, the authors prove novel asymptotic results for Wasserstein barycenters over one-dimensional distributions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about solving a problem where we don’t have all the information we need to understand something. It’s like trying to fill in missing puzzle pieces. The authors came up with a new way to do this by using special tools that help us match similar things together. They tested their method and found it works really well for getting accurate answers and making predictions. This is important because it can be used in many different areas, such as finance or climate modeling. |
Keywords
» Artificial intelligence » Probability
