Repro Samples Method for Model-Free Inference in High-Dimensional Binary Classification

Abstract: This paper presents a novel method for statistical inference in high-dimensional binary models with unspecified structure, where we leverage a (potentially misspecified) sparsity-constrained working generalized linear model (GLM) to facilitate the inference process. Our method is based on the repro samples framework, which generates artificial samples that mimic the actual data-generating process. Our inference targets include the model support, case probabilities, and the oracle regression coefficients defined in the working GLM. The proposed method has three major advantages. First, this approach is model-free, that is, it does not rely on specific model assumptions such as logistic or probit regression, nor does it require sparsity assumptions on the underlying model. Second, for model support, we construct a model candidate set for the most influential covariates that achieves guaranteed coverage under a weak signal strength assumption. Third, for oracle regression coefficients, we establish confidence sets for any group of linear combinations of regression coefficients. Simulation results demonstrate that the proposed method produces valid and small model candidate sets. It also achieves better coverage for regression coefficients than the state-of-the-art debiasing methods when the working model is the actual model that generates the sample data. Additionally, we analyze single-cell RNA-seq data on the immune response. Besides identifying genes previously proven 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.