High-dimensional non-Gaussian single index models via thresholded score function estimation

Zhuoran Yang; Krishnakumar Balasubramanian; Han Liu

High-dimensional non-Gaussian single index models via thresholded score function estimation

Zhuoran Yang, Krishnakumar Balasubramanian, Han Liu^*

^*Corresponding author for this work

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

We consider estimating the parametric component of single index models in high dimensions. Compared with existing work, we do not require the covariate to be normally distributed. Utilizing Stein's Lemma, we propose estimators based on the score function of the covariate. Moreover, to handle score function and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. Under a bounded fourth moment condition, we establish optimal statistical rates of convergence for the proposed estimators. Extensive numerical experiments are provided to back up our theory.

Original language	English (US)
Title of host publication	34th International Conference on Machine Learning, ICML 2017
Publisher	International Machine Learning Society (IMLS)
Pages	5878-5887
Number of pages	10
ISBN (Electronic)	9781510855144
State	Published - 2017
Event	34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia Duration: Aug 6 2017 → Aug 11 2017

Publication series

Name	34th International Conference on Machine Learning, ICML 2017
Volume	8

Other

Other	34th International Conference on Machine Learning, ICML 2017
Country/Territory	Australia
City	Sydney
Period	8/6/17 → 8/11/17

ASJC Scopus subject areas

Computational Theory and Mathematics
Human-Computer Interaction
Software

Cite this

@inproceedings{12b7aaa894bd483da063d2101f46db53,

title = "High-dimensional non-Gaussian single index models via thresholded score function estimation",

abstract = "We consider estimating the parametric component of single index models in high dimensions. Compared with existing work, we do not require the covariate to be normally distributed. Utilizing Stein's Lemma, we propose estimators based on the score function of the covariate. Moreover, to handle score function and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. Under a bounded fourth moment condition, we establish optimal statistical rates of convergence for the proposed estimators. Extensive numerical experiments are provided to back up our theory.",

author = "Zhuoran Yang and Krishnakumar Balasubramanian and Han Liu",

year = "2017",

language = "English (US)",

series = "34th International Conference on Machine Learning, ICML 2017",

publisher = "International Machine Learning Society (IMLS)",

pages = "5878--5887",

booktitle = "34th International Conference on Machine Learning, ICML 2017",

}

Yang, Z, Balasubramanian, K & Liu, H 2017, High-dimensional non-Gaussian single index models via thresholded score function estimation. in 34th International Conference on Machine Learning, ICML 2017. 34th International Conference on Machine Learning, ICML 2017, vol. 8, International Machine Learning Society (IMLS), pp. 5878-5887, 34th International Conference on Machine Learning, ICML 2017, Sydney, Australia, 8/6/17.

High-dimensional non-Gaussian single index models via thresholded score function estimation. / Yang, Zhuoran; Balasubramanian, Krishnakumar; Liu, Han.
34th International Conference on Machine Learning, ICML 2017. International Machine Learning Society (IMLS), 2017. p. 5878-5887 (34th International Conference on Machine Learning, ICML 2017; Vol. 8).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - High-dimensional non-Gaussian single index models via thresholded score function estimation

AU - Yang, Zhuoran

AU - Balasubramanian, Krishnakumar

AU - Liu, Han

PY - 2017

Y1 - 2017

N2 - We consider estimating the parametric component of single index models in high dimensions. Compared with existing work, we do not require the covariate to be normally distributed. Utilizing Stein's Lemma, we propose estimators based on the score function of the covariate. Moreover, to handle score function and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. Under a bounded fourth moment condition, we establish optimal statistical rates of convergence for the proposed estimators. Extensive numerical experiments are provided to back up our theory.

AB - We consider estimating the parametric component of single index models in high dimensions. Compared with existing work, we do not require the covariate to be normally distributed. Utilizing Stein's Lemma, we propose estimators based on the score function of the covariate. Moreover, to handle score function and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. Under a bounded fourth moment condition, we establish optimal statistical rates of convergence for the proposed estimators. Extensive numerical experiments are provided to back up our theory.

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M3 - Conference contribution

AN - SCOPUS:85048548290

T3 - 34th International Conference on Machine Learning, ICML 2017

SP - 5878

EP - 5887

BT - 34th International Conference on Machine Learning, ICML 2017

PB - International Machine Learning Society (IMLS)

T2 - 34th International Conference on Machine Learning, ICML 2017

Y2 - 6 August 2017 through 11 August 2017

ER -

High-dimensional non-Gaussian single index models via thresholded score function estimation

Abstract

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ASJC Scopus subject areas

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