An $\ell_{\infty}$ Eigenvector Perturbation Bound and Its Application
Authors: Jianqing Fan, Weichen Wang, Yiqiao Zhong
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our theoretical results are verified through extensive numerical experiments. Keywords: Matrix perturbation theory, Incoherence, Low-rank matrices, Sparsity, Approximate factor model |
| Researcher Affiliation | Academia | Jianqing Fan EMAIL Weichen Wang EMAIL Yiqiao Zhong EMAIL Department of Operations Research and Financial Engineering Princeton University Princeton, NJ 08544, USA |
| Pseudocode | No | The paper describes methods in prose (e.g., in Section 3.3 'The generic POET procedure encompasses three steps:') but does not include any clearly labeled pseudocode or algorithm blocks with structured formatting. |
| Open Source Code | No | The paper does not provide an explicit statement about the release of source code or a link to a code repository for the methodology described. The provided links are for the paper's license and attribution requirements, not for source code. |
| Open Datasets | No | The simulation section (Section 4) describes how data was generated synthetically for the experiments (e.g., 'sample a d d random matrix with iid standard normal variables', 'multivariate t-distribution'), rather than using publicly available datasets. No specific links or citations to open datasets are provided for the experimental evaluation. |
| Dataset Splits | No | The paper uses synthetic data generated for simulations, so explicit training/test/validation dataset splits are not applicable or described. The simulation section (Section 4) mentions generating 'n samples' but does not specify any data partitioning for model training or evaluation reproducibility in the context of standard dataset splits. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, memory, or computational environment used for running the simulations described in Section 4. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., programming languages, libraries, or frameworks) used for conducting the simulations. |
| Experiment Setup | Yes | In Section 4.1, the paper states: 'We let the matrix size d run from 200 to 2000 by an increment of 200. We fix the rank of A to be 3 (r = 3)... eigengap γ in {10, 50, 100, 500}'. For perturbation matrices, 's = 10, L = 3'. In Section 4.2: 'For the thresholding parameter, we used τ = 2 p log d/n'. |