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.