On the Saturation Effect of Kernel Ridge Regression
Authors: Yicheng Li, Haobo Zhang, Qian Lin
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we illustrate the saturation effect through a toy example. We conduct further experiments with different kernels and report them in Section E. The results are also approving. |
| Researcher Affiliation | Collaboration | Yicheng Li & Haobo Zhang Center for Statistical Science, Department of Industrial Engineering Tsinghua University, Beijing, China {liyc22,zhang-hb21}@mails.tsinghua.edu.cn Qian Lin Center for Statistical Science, Department of Industrial Engineering Tsinghua University, Beijing, China and Beijing Academy of Artificial Intelligence, Beijing, China qianlin@tsinghua.edu.cn |
| Pseudocode | No | The paper describes algorithms and mathematical derivations but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement about releasing open-source code or a link to a code repository for the methodology described. |
| Open Datasets | No | The paper uses a self-generated toy example with the specific kernel k(x, y) = min(x, y) on X = [0, 1] with a uniform distribution µ, and a data generation model y = f (x) + σε, but does not provide concrete access information (e.g., link, DOI, citation) for a publicly available dataset. |
| Dataset Splits | No | The paper mentions observing 'n i.i.d. samples' and performing '100 trials' for each n, but it does not specify any training, validation, or test dataset splits or percentages. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers, such as programming languages, libraries, or solvers. |
| Experiment Setup | Yes | For various α s, we choose the regularization parameter in KRR as λ = cn 1 α+β for a fixed constant c, and set the stopping time in the gradient flow by t = λ 1. For the generalization error ˆf f ρ 2 L2, we numerically compute the integration (L2-norm) by Simpson s formula with N n points. |