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An l eigenvector perturbation bound and its application to robust covariance estimation

Jianqing Fan Weichen Wang Yiqiao Zhong

Statistics Theory and Methods mathscidoc:1912.43368

Journal of Machine Learning Research, 18, (207), 1-42, 2018.4
In statistics and machine learning, we are interested in the eigenvectors (or singular vectors) of certain matrices (eg covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. The Davis-Kahan sin theorem is often used to bound the difference between the eigenvectors of a matrix A and those of a perturbed matrix A= A+ E, in terms of l2 norm. In this paper, we prove that when A is a low-rank and incoherent matrix, the l norm perturbation bound of singular vectors (or eigenvectors in the symmetric case) is smaller by a factor of
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@inproceedings{jianqing2018an,
  title={An l eigenvector perturbation bound and its application to robust covariance estimation},
  author={Jianqing Fan, Weichen Wang, and Yiqiao Zhong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114001747170928},
  booktitle={Journal of Machine Learning Research},
  volume={18},
  number={207},
  pages={1-42},
  year={2018},
}
Jianqing Fan, Weichen Wang, and Yiqiao Zhong. An l eigenvector perturbation bound and its application to robust covariance estimation. 2018. Vol. 18. In Journal of Machine Learning Research. pp.1-42. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114001747170928.
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