Stable variable ranking and selection in regularized logistic regression for severely imbalanced big binary data

Abstract

We develop a novel covariate ranking and selection algorithm for regularized ordinary logistic regression (OLR) models in the presence of severe class-imbalance in high dimensional datasets with correlated signal and noise covariates. Class-imbalance is resolved using response-based subsampling which we also employ to achieve stability in variable selection by creating an ensemble of regularized OLR models fitted to subsampled (and balanced) datasets. The regularization methods considered in our study include Lasso, adaptive Lasso (adaLasso) and ridge regression. Our methodology is versatile in the sense that it works effectively for regularization techniques involving both hard- (e.g. Lasso) and soft-shrinkage (e.g. ridge) of the regression coefficients. We assess selection performance by conducting a detailed simulation experiment involving varying moderate-to-severe class-imbalance ratios and highly correlated continuous and discrete signal and noise covariates. Simulation results show that our algorithm is robust against severe class-imbalance under the presence of highly correlated covariates, and consistently achieves stable and accurate variable selection with very low false discovery rate. We illustrate our methodology using a case study involving a severely imbalanced high-dimensional wildland fire occurrence dataset comprising 13 million instances. The case study and simulation results demonstrate that our framework provides a robust approach to variable selection in severely imbalanced big binary data.