Entrywise eigenvector analysis of random matrices with low expected rank

Emmanuel Abbe Jianqing Fan Kaizheng Wang Yiqiao Zhong

Machine Learning mathscidoc:1912.43331

arXiv preprint arXiv:1709.09565, 2017.9
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of results provide tight bounds on the average errors between empirical and population statistics of eigenvectors, fewer results are tight for entrywise analyses, which are critical for a number of problems such as community detection and ranking.
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@inproceedings{emmanuel2017entrywise,
  title={Entrywise eigenvector analysis of random matrices with low expected rank},
  author={Emmanuel Abbe, Jianqing Fan, Kaizheng Wang, and Yiqiao Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113744646859891},
  booktitle={arXiv preprint arXiv:1709.09565},
  year={2017},
}
Emmanuel Abbe, Jianqing Fan, Kaizheng Wang, and Yiqiao Zhong. Entrywise eigenvector analysis of random matrices with low expected rank. 2017. In arXiv preprint arXiv:1709.09565. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113744646859891.
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