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Learning Non-Gaussian Multi-Index Model via Second-Order Stein’s Method
Abstract View the Paper

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.


Venue
2017 NIPS
Publication Time
Dec 2017
Authors
Zhuoran Yang, krishnakumar balasubramanian, Zhaoran Wang , Han Liu