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Statistical inferences for high-dimensional regression models have beenextensively studied for their wide applications ranging from genomics,neuroscience, to economics. However, in practice, there are often potentialunmeasured confounders associated with both the response and covariates, whichcan lead to invalidity of standard debiasing methods. This paper focuses on ageneralized linear regression framework with hidden confounding and proposes adebiasing approach to address this high-dimensional problem, by adjusting forthe effects induced by the unmeasured confounders. We establish consistency andasymptotic normality for the proposed debiased estimator. The finite sampleperformance of the proposed method is demonstrated through extensive numericalstudies and an application to a genetic data set.

High-Dimensional Inference for Generalized Linear Models with Hidden Confounding