On the Optimality of Misspecified Kernel Ridge Regression
Authors: Haobo Zhang, Yicheng Li, Weihao Lu, Qian Lin
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In our experiments, we aim to verify that for functions f ρ [H]s but not in L , the KRR estimator can still achieve the convergence rate n sβ sβ+1 . We show the results for both Sobolev RKHS, and general RKHS with uniformly bounded eigenfunctions mentioned in Remark 3.3. We numerically compute the generalization error ˆf f L2 by Simpson s formula with N n testing points. For each n, we repeat the experiments 50 times and present the average generalization error as well as the region within one standard deviation. |
| Researcher Affiliation | Collaboration | 1Center for Statistical Science, Department of Industrial Engineering, Tsinghua University 2Beijing Academy of Artificial Intelligence, Beijing, China. |
| Pseudocode | No | The paper provides a 'Sketch of proof' which describes the mathematical steps but does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about making its source code publicly available or providing a link to a code repository for its methodology. |
| Open Datasets | No | The paper generates synthetic data based on mathematical functions and distributions (e.g., 'x U[0, 1]') but does not refer to or provide access information for a publicly available or open dataset. |
| Dataset Splits | Yes | We also did another experiment that used cross validation to choose the regularization parameter. Figure 3 in Appendix F shows a similar result as Figure 1. In Figure 3 (b), we use 5-fold cross validation to choose the regularization parameter in KRR and present the logarithmic errors and sample sizes. |
| Hardware Specification | No | The paper does not specify any details regarding the hardware (e.g., CPU, GPU models, memory) used for conducting the experiments. |
| Software Dependencies | No | The paper does not list specific versions for any software dependencies, libraries, or frameworks used in the experiments. |
| Experiment Setup | Yes | We choose the regularization parameter as λ = cn β sβ+1 = cn 10/9 for a fixed c. We try different values of c, Figure 1 presents the convergence curve under the best choice of c. |