Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay
Authors: Yicheng Li, haobo Zhang, Qian Lin
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we consider numerical experiments on a toy model to verify our theory. For some f , we generate data from the model y = f (x) + ε where ε N(0, 0.05) and perform KRR with λ = cn θ for different θ s with some fixed constant c. Then, we numerically compute the variance, bias and excess risk by Simpson s formula with N n nodes. Repeating the experiment for n ranged in 1000 to 5000, we can estimate the convergence rate r by a logarithmic least-squares log err = r log n + b on the values (variance, bias and excess risk). The results are collected in Table 1 on page 10. |
| Researcher Affiliation | Academia | Yicheng Li, Haobo Zhang Center for Statistical Science, Department of Industrial Engineering Tsinghua University, Beijing, China EMAIL Qian Lin Center for Statistical Science, Department of Industrial Engineering Tsinghua University, Beijing, China EMAIL Qian Lin also affiliates with Beijing Academy of Artificial Intelligence, Beijing, China |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about releasing open-source code or provide links to a code repository for the described methodology. |
| Open Datasets | No | The paper uses synthetic data generated from a toy model ("Let us consider the kernel k(x, y) = min(x, y) and x U[0, 1]... For some f , we generate data from the model y = f (x) + ε"), rather than a publicly available dataset. |
| Dataset Splits | No | The paper does not explicitly provide training/validation/test dataset splits. It generates synthetic data to numerically verify theoretical results, stating: "Repeating the experiment for n ranged in 1000 to 5000." |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments. |
| Software Dependencies | No | The paper does not list specific software components with their version numbers that would be needed to reproduce the experiment. |
| Experiment Setup | Yes | For some f , we generate data from the model y = f (x) + ε where ε N(0, 0.05) and perform KRR with λ = cn θ for different θ s with some fixed constant c. ... Note that for each setting, we tried different c s in the regularization parameter λ = cn θ and show the curves under the best choice of c (c = 0.005). |