QUADRO: A supervised dimension reduction method via Rayleigh quotient optimization

Jianqing Fan Zheng Tracy Ke Han Liu Lucy Xia

Statistics Theory and Methods mathscidoc:1912.43355

Annals of statistics, 43, (4), 1498, 2015
We propose a novel Rayleigh quotient based sparse quadratic dimension reduction methodnamed QUADRO (Qua dratic D imension R eduction via Rayleigh O ptimization)for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are
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@inproceedings{jianqing2015quadro:,
  title={QUADRO: A supervised dimension reduction method via Rayleigh quotient optimization},
  author={Jianqing Fan, Zheng Tracy Ke, Han Liu, and Lucy Xia},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113914704047915},
  booktitle={Annals of statistics},
  volume={43},
  number={4},
  pages={1498},
  year={2015},
}
Jianqing Fan, Zheng Tracy Ke, Han Liu, and Lucy Xia. QUADRO: A supervised dimension reduction method via Rayleigh quotient optimization. 2015. Vol. 43. In Annals of statistics. pp.1498. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113914704047915.
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