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; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
On the Saturation Effects of Spectral Algorithms in Large Dimensions
Authors: Weihao Lu, haobo Zhang, Yicheng Li, Qian Lin
NeurIPS 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A.2 Numerical experiments We conducted two experiments using two specific kernels: the RBF kernel and the NTK kernel. Experiment 1 was designed to confirm the optimal rate of kernel gradient flow and KRR when s = 1. Experiment 2 was designed to illustrate the saturation effect of KRR when s > 1. |
| Researcher Affiliation | Academia | Weihao Lu Department of Statistics and Data Science Tsinghua University Beijing, China 100084 EMAIL Haobo Zhang Department of Statistics and Data Science Tsinghua University Beijing, China 100084 EMAIL Yicheng Li Department of Statistics and Data Science Tsinghua University Beijing, China 100084 EMAIL Qian Lin Department of Statistics and Data Science Tsinghua University Beijing, China 100084 EMAIL |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found. |
| Open Source Code | No | The NeurIPS checklist states 'The paper does not include experiments requiring code.' |
| Open Datasets | No | We used the following data generation procedure: yi = f (xi) + ϵi, i = 1, . . . , n, where each xi is i.i.d. sampled from the uniform distribution on Sd, and ϵi i.i.d. N(0, 1). This indicates synthetic data generation, not a publicly accessible dataset. |
| Dataset Splits | Yes | We use 5-fold cross-validation to select the regularization parameter λ in kernel ridge regression. The alternative values of λ in cross-validation are C2n C3, where C2 {0.001, 0.005, 0.01, 0.1, 0.5, 1, 2, 5, 10, 40, 100, 300, 1000}, C3 {0.1, 0.2, . . . , 1.5}. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) were provided for running the experiments. |
| Software Dependencies | No | No specific software dependencies with version numbers (e.g., Python, PyTorch, TensorFlow versions) were explicitly mentioned. |
| Experiment Setup | Yes | We choose the stopping time t in kernel gradient flow as C1n0.5, where C1 {0.001, 0.01, 0.1, 1, 10, 100, 1000}. We use 5-fold cross-validation to select the regularization parameter λ in kernel ridge regression. The alternative values of λ in cross-validation are C2n C3, where C2 {0.001, 0.005, 0.01, 0.1, 0.5, 1, 2, 5, 10, 40, 100, 300, 1000}, C3 {0.1, 0.2, . . . , 1.5}. |