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Estimating High-dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma
Zhuoran Yang · Krishnakumar Balasubramanian · Zhaoran Wang · Han Liu

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #72

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.

Author Information

Zhuoran Yang (Princeton University)
Krishnakumar Balasubramanian (University of California, Davis)
Zhaoran Wang (Princeton, Phd student)
Han Liu (Tencent AI Lab)

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