Optimal and Safe Estimation for High-Dimensional Semi-Supervised Learning

Deng, Siyi; Ning, Yang; Zhao, Jiwei; Zhang, Heping

doi:10.1080/01621459.2023.2277409

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…Concerning statistical inference for high-dimensional regression models under the fully observed settings, there are a number of developments based on bias correction of regularized estimators, including Javanmard and Montanari (2014), van de Geer et al ( 2014), Zhang and Zhang (2014), Ning and Liu (2017), Montanari (2018), andNeykov et al (2018), among many others. More recently, high-dimensional inference problems with the partially observed response have been studied (Bellec et al, 2018;Zhang and Bradic, 2019;Cai and Guo, 2020;Deng et al, 2020). However, none of these methods addresses the problem of missing covariates; in particular, to the best of our knowledge, there is no existing method that focuses on the statistical inference for high dimensional regression with blockwise missing data.…”

Section: Related Workmentioning

confidence: 99%

Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data

Xue¹,

Ma²,

Li³

2025

STAT SINICA

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Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.

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