Summary of Optimal Sampling For Least-squares Approximation, by Ben Adcock
Optimal sampling for least-squares approximation
by Ben Adcock
First submitted to arxiv on: 4 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA)
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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 reviews recent progress on optimal sampling for least-squares approximation in arbitrary linear spaces. The authors introduce the Christoffel function as a key quantity in the analysis of (weighted) least-squares approximation from random samples, showing how it can be used to construct sampling strategies that possess near-optimal sample complexity. The number of samples scales log-linearly with the dimension of the approximation space. The paper discusses variations, extensions, and connections to approximation theory, machine learning, information-based complexity, and numerical linear algebra. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about finding the best way to collect data for a mathematical problem called least-squares approximation. This method helps us figure out an unknown function from some given data. The authors explain how we can choose where to take these data points to get the most accurate results. They use a special formula, called Christoffel’s function, to do this and show that it works really well. |
Keywords
* Artificial intelligence * Machine learning
