Summary of Generalization Error Of Spectral Algorithms, by Maksim Velikanov et al.
Generalization error of spectral algorithms
by Maksim Velikanov, Maxim Panov, Dmitry Yarotsky
First submitted to arxiv on: 18 Mar 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 proposed paper investigates the asymptotic estimation of generalization error for kernel methods, particularly those trained with spectral algorithms that include kernel ridge regression (KRR) and gradient descent (GD). The authors consider two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. They derive the generalization error as a functional of learning profile h(λ) and use this framework to analyze the loss asymptotics for both noisy and noiseless observations. The paper also explores the localization of the loss on certain spectral scales, providing new insights into the KRR saturation phenomenon. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how well kernel methods can generalize when trained with different algorithms. It’s like trying to predict what a person will look like based on their family photos, but instead of faces, it’s numbers and patterns in data. The authors use special math formulas to figure out how good these predictions are likely to be, and they find some surprising things. For example, the quality of the predictions depends on which type of algorithm is used, and how much noise (or randomness) there is in the data. |
Keywords
* Artificial intelligence * Generalization * Gradient descent * Regression * Translation
