Coherence-free Entrywise Estimation of Eigenvectors in Low-rank Signal-plus-noise Matrix Models
Authors: Hao Yan, Keith Levin
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical experiments. We turn to a brief experimental exploration of our theoretical results. |
| Researcher Affiliation | Academia | Hao Yan Department of Statistics University of Wisconsin Madison Madison, WI 53706 United States of America hyan84@wisc.edu. Keith Levin Department of Statistics University of Wisconsin Madison Madison, WI 53706 United States of America kdlevin@wisc.edu |
| Pseudocode | Yes | Algorithm 1 Coherence-free eigenvector estimation algorithm. Input: Observed matrix Y Rn n; leading eigenvalue estimate bλ; parameter β > 0. Output: bu Rn |
| Open Source Code | Yes | in addition to the algorithmic descriptions in Sections 2 and 3 and the details in Section 5, we have included code for running all reported experiments in our supplemental materials. |
| Open Datasets | No | We consider three distributions for the entries of W : Gaussian, Laplacian and Rademacher, all scaled to have variance σ2 = 1. We consider two approaches to generating u . |
| Dataset Splits | No | We report the mean of 20 independent trials for each combination of problem size n, magnitude a and methods for generating u and W . |
| Hardware Specification | No | All experiments were run in a distributed environment on commodity hardware without GPUs. In total, the experiments reported below used 3425 compute-hours. Mean memory usage was 3.5 GB, with a maximum of 11 GB. |
| Software Dependencies | No | The paper mentions 'open source software tools' in the NeurIPS checklist but does not provide specific software or library version numbers. |
| Experiment Setup | Yes | We take λ = n log n in all experiments, matching the rate in Remark 1. We consider three distributions for the entries of W : Gaussian, Laplacian and Rademacher, all scaled to have variance σ2 = 1. |