Summary of Dimension-free Deterministic Equivalents and Scaling Laws For Random Feature Regression, by Leonardo Defilippis et al.
Dimension-free deterministic equivalents and scaling laws for random feature regression
by Leonardo Defilippis, Bruno Loureiro, Theodor Misiakiewicz
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
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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 This paper investigates the generalization performance of random feature ridge regression (RFRR) and derives a deterministic equivalent for the test error of RFRR. The researchers show that under certain conditions, the test error is well-approximated by a closed-form expression dependent on feature map eigenvalues, providing a non-asymptotic, multiplicative, and dimension-independent guarantee. This approximation holds broadly and is empirically validated on various real and synthetic datasets. As an application, the paper derives sharp excess error rates under standard power-law assumptions of the spectrum and target decay, providing a tight result for the smallest number of features achieving optimal minimax error rate. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how well random feature ridge regression (RFRR) works in real-world situations. The researchers find a way to predict how well RFRR will perform without needing to know all the details about the data. They test this idea on many different datasets and show that it’s accurate. This is important because RFRR can be used in many different areas, like predicting stock prices or recognizing objects in pictures. The paper also helps us understand when RFRR is likely to work well or poorly. |
Keywords
» Artificial intelligence » Feature map » Generalization » Regression
