When the sample size is equal or less than the number of covariates, traditional logistic regression is plugged with degenerates and wild behavior. Therefore, classification results are not reliable. We use finite population Bayesian bootstrapping for resampling, such that the new sample size becomes greater than the number of covariates. Combining original samples and the mean of simulated data, and also applying sufficient dimension reduction method, we introduce a new algorithm based on traditional logistic regression for high-dimensional binary classification. Then, we compare the proposed algorithm with the regularized logistic models and other popular classification algorithms using both simulated and real data.
