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Regularity properties of high-dimensional covariate matrices

Edgar Dobriban Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43428

arXiv preprint arXiv:1305.5198, 2013.5
Regularity properties such as the incoherence condition, the restricted isometry property, compatibility, restricted eigenvalue and iq sensitivity of covariate matrices play a pivotal role in high-dimensional regression and compressed sensing. Yet, like computing the spark of a matrix, we first show that it is NP-hard to check the conditions involving all submatrices of a given size.
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@inproceedings{edgar2013regularity,
  title={Regularity properties of high-dimensional covariate matrices},
  author={Edgar Dobriban, and Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114349644890988},
  booktitle={arXiv preprint arXiv:1305.5198},
  year={2013},
}
Edgar Dobriban, and Jianqing Fan. Regularity properties of high-dimensional covariate matrices. 2013. In arXiv preprint arXiv:1305.5198. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114349644890988.
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