  This paper presents a novel method to make statistical inferences for both
the model support and regression coefficients in a high-dimensional logistic
regression model. Our method is based on the repro samples framework, in which
we conduct statistical inference by generating artificial samples mimicking the
actual data-generating process. The proposed method has two major advantages.
Firstly, for model support, we introduce the first method for constructing
model confidence set in a high-dimensional setting and the proposed method only
requires a weak signal strength assumption. Secondly, in terms of regression
coefficients, we establish confidence sets for any group of linear combinations
of regression coefficients. Our simulation results demonstrate that the
proposed method produces valid and small model confidence sets and achieves
better coverage for regression coefficients than the state-of-the-art debiasing
methods. Additionally, we analyze single-cell RNA-seq data on the immune
response. Besides identifying genes previously proved as relevant in the
literature, our method also discovers a significant gene that has not been
studied before, revealing a potential new direction in understanding cellular
immune response mechanisms.
