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.

翻译：本文提出了一种用于同时进行变量和组选择的高维新方法，称为稀疏组SLOPE（SGS）。SGS通过将SLOPE模型融入稀疏组框架并利用分组信息，实现了在变量和组两个层面上的错误发现率控制。本文实现了一种适用于高斯分布和二项分布响应变量的近端算法来拟合SGS模型。通过对合成数据集和真实数据集的分析，发现所提出的SGS方法在双层选择和预测精度方面优于其他现有的基于lasso和SLOPE的模型。此外，本文还提出并探讨了用于选择正则化模型调优参数的模型选择和噪声估计方法。