Feature augmentation via nonparametrics and selection (FANS) in high-dimensional classification

Jianqing Fan Yang Feng Jiancheng Jiang Xin Tong

Statistics Theory and Methods mathscidoc:1912.43366

Journal of the American Statistical Association, 111, (513), 275-287, 2016.1
We propose a high-dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called feature augmentation via nonparametrics and selection (FANS). We motivate FANS by generalizing the naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are
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@inproceedings{jianqing2016feature,
  title={Feature augmentation via nonparametrics and selection (FANS) in high-dimensional classification},
  author={Jianqing Fan, Yang Feng, Jiancheng Jiang, and Xin Tong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113954267457926},
  booktitle={Journal of the American Statistical Association},
  volume={111},
  number={513},
  pages={275-287},
  year={2016},
}
Jianqing Fan, Yang Feng, Jiancheng Jiang, and Xin Tong. Feature augmentation via nonparametrics and selection (FANS) in high-dimensional classification. 2016. Vol. 111. In Journal of the American Statistical Association. pp.275-287. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113954267457926.
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