Estimating High-dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma

Zhuoran Yang; Krishnakumar Balasubramanian; Zhaoran Wang; Han Liu

NeurIPS 2017poster23 citations

Estimating High-dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma

Zhuoran Yang, Krishnakumar Balasubramanian, Zhaoran Wang, Han Liu

Abstract

We consider estimating the parametric components of semiparametric multi-index models in high dimensions. To bypass the requirements of Gaussianity or elliptical symmetry of covariates in existing methods, we propose to leverage a second-order Stein’s method with score function-based corrections. We prove that our estimator achieves a near-optimal statistical rate of convergence even when the score function or the response variable is heavy-tailed. To establish the key concentration results, we develop a data-driven truncation argument that may be of independent interest. We supplement our theoretical findings with simulations.

BibTeX

@inproceedings{NIPS2017_4db0f8b0,
 author = {Yang, Zhuoran and Balasubramanian, Krishnakumar and Wang, Zhaoran and Liu, Han},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {I. Guyon and U. Von Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Estimating High-dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma},
 url = {https://proceedings.neurips.cc/paper_files/paper/2017/file/4db0f8b0fc895da263fd77fc8aecabe4-Paper.pdf},
 volume = {30},
 year = {2017}
}