Bayesian empirical likelihood for UltraHigh-dimensional variable selection with application to drug sensitivity

Predicting drug sensitivity and selecting informative biomarkers are fundamental challenges in precision oncology. These tasks are complicated by the ultrahigh-dimensional nature of omics data, where the number of covariates p far exceeds the sample size n. While variable selection methods are widely used, traditional high-dimensional regression techniques often rely on the assumption of Gaussian noise, which is frequently violated in real-world omics datasets. To overcome these limitations, we propose a Bayesian empirical likelihood approach (BEL_HD) for variable selection and prediction in a semiparametric framework. BEL_HD avoids strict distributional assumptions by utilizing estimating equations and imposes joint regularization on both regression coefficients and the Lagrange multipliers to promote sparsity. We also introduce an efficient active set MCMC algorithm that enables scalable inference in ultrahigh-dimensional spaces. Through simulations and real-data applications, including a case study on leukemia drug sensitivity, BEL_HD demonstrates superior predictive performance and selects biologically interpretable features. Our method combines the flexibility of empirical likelihood with the inferential benefits of Bayesian modeling, offering a robust and extensible tool for high-dimensional biomedical research.