High-dimensional Inference for Generalized Linear Models with Hidden Confounding

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. In practice, there are often potential unmeasured confounders associated with both the response and covariates, leading to the invalidity of the standard debiasing methods. This paper focuses on a generalized linear regression framework with hidden confounding and proposes a debiasing approach to address this high-dimensional problem by adjusting for effects induced by the unmeasured confounders. We establish consistency and asymptotic normality for the proposed debiased estimator. The finite sample performance of the proposed method is demonstrated via extensive numerical studies and an application to a genetic dataset.