I-LAMM for sparse learning: Simultaneous control of algorithmic complexity and statistical error

Jianqing Fan Han Liu Qiang Sun Tong Zhang

Numerical Analysis and Scientific Computing mathscidoc:1912.43348

Annals of statistics, 46, (2), 814, 2018.4
We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second stage by iteratively solving a sequence of convex programs with smaller precision tolerances. Theoretically, we establish a phase transition: the first stage has a sublinear iteration complexity, while the second stage achieves an improved linear rate of convergence. Though this framework is completely algorithmic, it provides solutions with optimal statistical performances and controlled algorithmic complexity for a large family
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@inproceedings{jianqing2018i-lamm,
  title={I-LAMM for sparse learning: Simultaneous control of algorithmic complexity and statistical error},
  author={Jianqing Fan, Han Liu, Qiang Sun, and Tong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113849645173908},
  booktitle={Annals of statistics},
  volume={46},
  number={2},
  pages={814},
  year={2018},
}
Jianqing Fan, Han Liu, Qiang Sun, and Tong Zhang. I-LAMM for sparse learning: Simultaneous control of algorithmic complexity and statistical error. 2018. Vol. 46. In Annals of statistics. pp.814. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113849645173908.
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