High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion

Chen，Xin1; Deng，Chang2; He，Shuaida1; Wu，Runxiong3; Zhang，Jia4

2024-04-01

10.1007/s11222-024-10399-4

Statistics and Computing   影响因子和分区

0960-3174

1573-1375

Hilbert-Schmidt Independence Criterion (HSIC) has recently been introduced to the field of single-index models to estimate the directions. Compared with other well-established methods, the HSIC based method requires relatively weak conditions. However, its performance has not yet been studied in the prevalent high-dimensional scenarios, where the number of covariates can be much larger than the sample size. In this article, based on HSIC, we propose to estimate the possibly sparse directions in the high-dimensional single-index models through a parameter reformulation. Our approach estimates the subspace of the direction directly and performs variable selection simultaneously. Due to the non-convexity of the objective function and the complexity of the constraints, a majorize-minimize algorithm together with the linearized alternating direction method of multipliers is developed to solve the optimization problem. Since it does not involve the inverse of the covariance matrix, the algorithm can naturally handle large p small n scenarios. Through extensive simulation studies and a real data analysis, we show that our proposal is efficient and effective in the high-dimensional settings. The Matlab codes for this method are available online.

Hilbert-Schmidt independence criterion Large p small n Majorization-minimization Single-index models Sufficient dimension reduction Variable selection

SCI

英语

第一

COMPUTER SCIENCE

2-s2.0-85186175535

Scopus

1.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,China
2.Booth School of Business,University of Chicago,Chicago,United States
3.College of Engineering,University of California,Davis,United States
4.Joint Laboratory of Data Science and Business Intelligence,Southwestern University of Finance and Economics,Chengdu,China

Chen，Xin,Deng，Chang,He，Shuaida,等. High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion[J]. Statistics and Computing,2024,34(2).

Chen，Xin,Deng，Chang,He，Shuaida,Wu，Runxiong,&Zhang，Jia.(2024).High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion.Statistics and Computing,34(2).

Chen，Xin,et al."High-dimensional sparse single–index regression via Hilbert–Schmidt independence criterion".Statistics and Computing 34.2(2024).