Summary of Learning on Manifolds Without Manifold Learning, by H. N. Mhaskar and Ryan O’dowd
Learning on manifolds without manifold learning
by H. N. Mhaskar, Ryan O’Dowd
First submitted to arxiv on: 20 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 a new approach to function approximation based on data drawn randomly from an unknown distribution. Building upon the manifold hypothesis, which assumes that the data is sampled from an unknown submanifold of high-dimensional Euclidean space, the authors propose a one-shot method that avoids estimating basic quantities of the data manifold. Instead, they project the unknown manifold as a submanifold of an ambient hypersphere and use localized spherical polynomial kernels to construct the approximation. The approach does not require preprocessing of the data and achieves optimal rates of approximation for relatively “rough” functions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to guess information about things we can’t see or touch, like a hidden surface in space. Imagine you have a big ball with many little balls attached to it – these little balls represent the things we don’t know much about. The researchers want to figure out how to find patterns on this hidden surface just by looking at the big ball and the way the little balls move around it. They found a clever way to do this without having to learn more about each little ball beforehand, which makes their method very useful for solving certain problems. |
Keywords
* Artificial intelligence * One shot
