Sparse-group SLOPE: adaptive bi-level selection with FDR-control

In this manuscript, a new high-dimensional approach for simultaneous variable and group selection is proposed, called sparse-group SLOPE (SGS). SGS achieves false discovery rate control at both variable and group levels by incorporating the SLOPE model into a sparse-group framework and exploiting grouping information. A proximal algorithm is implemented for fitting SGS that works for both Gaussian and Binomial distributed responses. Through the analysis of both synthetic and real datasets, the proposed SGS approach is found to outperform other existing lasso- and SLOPE-based models for bi-level selection and prediction accuracy. Further, model selection and noise estimation approaches for selecting the tuning parameter of the regularisation model are proposed and explored.