The optimality of kernel classifiers in Sobolev space
Authors: Jianfa Lai, zhifan Li, Dongming Huang, Qian Lin
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2η(x) 1 and apply the method to real datasets... Furthermore, we provide a method to estimate the interpolation space smoothness parameter s and also present some numerical results for neural network classification problems through simulation studies and real data analysis. |
| Researcher Affiliation | Academia | Jianfa Lai Tsinghua University, Beijing, China jianfalai@mail.tsinghua.edu.cn Zhifan Li Beijing Institute of Mathematical Sciences and Applications, Beijing, China zhifanli@bimsa.cn Dongming Huang National University of Singapore, Singapore stahd@nus.edu.sg Qian Lin Tsinghua University, Beijing, China qianlin@tsinghua.edu.cn |
| Pseudocode | No | The paper does not contain any blocks explicitly labeled as "Pseudocode" or "Algorithm". |
| Open Source Code | No | The paper does not provide any specific links to source code repositories or explicitly state that the code for the described methodology is open-source or publicly available. |
| Open Datasets | Yes | As an application of Truncation Estimation, we estimate the relative smoothness of real data sets with respect to the NTK defined in equation 11. The results are shown in Table 1. We can see that with respect to the NTK, MNIST has the largest relative smoothness while CIFAR-10 has the smallest one. This result aligns with the common knowledge that MNIST is the easiest dataset while CIFAR-10 is the most difficult one of these three datasets... Table 1: Truncation Estimation of the relative smoothness s of different real data sets with different NTKs. NTK L indicates the L-hidden-layer NTK. We only consider two classes of labels for each dataset: Label 1 and 7 for MNIST, trousers and sneakers for Fashion-MNIST, cars and horses for CIFAR-10. We randomly select 5,000 data points and choose the truncation point 100 to estimate s. |
| Dataset Splits | No | The paper describes using sample points for estimation and randomly selecting data points, but it does not specify traditional training, validation, or test dataset splits, nor does it describe cross-validation. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies, such as programming languages, libraries, or solvers with version numbers. |
| Experiment Setup | Yes | The experiment uses 5, 000 sample points and the truncation point is 100... We randomly select 5,000 data points and choose the truncation point 100 to estimate s... NTK L indicates the L-hidden-layer NTK. We only consider two classes of labels for each dataset: Label 1 and 7 for MNIST, trousers and sneakers for Fashion-MNIST, cars and horses for CIFAR-10. |