Distributed Semi-Supervised Inference for Generalized Linear Models With Block-Wise Missing Covariates

For a relatively small labeled dataset from high-dimensional generalized linear models with block-wise missing covariates and a large unlabeled dataset, we utilize a model-assisted approach in the labeled dataset to address the issue of block-wise missing covariates and then integrate the unlabeled data to construct estimation equations for the coefficients without any imputation. A lasso-penalized semi-supervised estimator is obtained, and then its debiased estimator is proposed to establish asymptotic normality/confidence intervals. When the labeled data are distributed in multiple machines independently and only some machines have unlabeled data, we further propose a distributed debiased semi-supervised estimator for estimation and inference. The finite sample performance of our proposed two estimators is studied through simulations and further illustrated with a breast cancer dataset.