Summary of Optimal Rates Of Kernel Ridge Regression Under Source Condition in Large Dimensions, by Haobo Zhang et al.
Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions
by Haobo Zhang, Yicheng Li, Weihao Lu, Qian Lin
First submitted to arxiv on: 2 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 large-dimensional behavior of kernel ridge regression (KRR), a type of neural network-inspired algorithm. The study focuses on understanding how KRR performs when the sample size is comparable to the dimensionality of the data, often referred to as the “big-data” regime. By analyzing the properties of the true function and the interpolation space of the reproducing kernel Hilbert space (RKHS), the authors derive exact bounds for the generalization error of KRR with an optimally chosen regularization parameter. The results show that when the source condition is small (s ≤ 1), KRR is minimax optimal, but when s > 1, it becomes suboptimal. The study also reveals periodic plateau and multiple descent behaviors in the curves of rate varying along γ. These findings unify previous works on kernel regression in large-dimensional settings. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how a type of machine learning algorithm called kernel ridge regression (KRR) performs when we have lots of data compared to the number of features. The researchers want to understand what happens when we try to use KRR for big datasets. They find out that if we’re in a certain situation, KRR works really well, but if we’re not, it doesn’t do as well. They also discover some interesting patterns in how KRR behaves. This work helps us understand how KRR can be used in different situations. |
Keywords
* Artificial intelligence * Generalization * Machine learning * Neural network * Regression * Regularization
