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Poster
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 #None
in Posters Tue »

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.

Keywords: Signal Processing · Frequentist Statistics · Convex Optimization

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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