Current high-throughput technologies provide a large amount of variables to describe a phenomenon. Only a few variables are generally sufficient to answer the question. Identify them in a high-dimensional Gaussian linear regression model is the one of the most-used statistical methods. In this article, we describe step-by-step the variable selection procedures built upon regularization paths. Regularization paths are obtained by combining a regularization function and an algorithm. Then, they are combined either with a model selection procedure using penalty functions or with a sampling strategy to obtain the final selected variables. We perform a comparison study by considering three simulation settings with various dependency structures on variables. %from the most classical to a most realistic one. In all the settings, we evaluate (i) the ability to discriminate between the active variables and the non-active variables along the regularization path (pROC-AUC), (ii) the prediction performance of the selected variable subset (MSE) and (iii) the relevance of the selected variables (recall, specificity, FDR). From the results, we provide recommendations on strategies to be favored depending on the characteristics of the problem at hand. We obtain that the regularization function Elastic-net provides most of the time better results than the $\ell_1$ one and the lars algorithm has to be privileged as the GD one. ESCV provides the best prediction performances. Bolasso and the knockoffs method are judicious choices to limit the selection of non-active variables while ensuring selection of enough active variables. Conversely, the data-driven penalties considered in this review are not to be favored. As for Tigress and LinSelect, they are conservative methods.

翻译：当前高通量技术提供了大量描述现象的变量，而通常仅需少数变量即可解答相关问题。在基于高维高斯线性回归模型中识别这些关键变量，是使用最广泛的统计方法之一。本文逐步阐述了基于正则化路径构建的变量选择流程。正则化路径通过结合正则化函数与算法获得，继而与基于惩罚函数的模型选择方法或采样策略相结合，最终确定选定的变量集。我们通过考虑三种具有不同变量依赖结构的仿真场景（从经典场景到更贴近实际的场景）开展比较研究。在所有场景中，我们评估了：（i）沿正则化路径区分活跃变量与非活跃变量的能力（pROC-AUC）；（ii）选定变量子集的预测性能（MSE）；（iii）选定变量的相关性（召回率、特异性、FDR）。基于实验结果，我们针对不同问题特征提出了算法策略的选择建议。研究发现：弹性网络正则化函数在多数情况下优于ℓ₁正则化；相较于GD算法应优先采用lars算法；ESCV方法展现了最佳预测性能；Bolasso与knockoffs方法在限制非活跃变量选择的同时，能有效确保足够数量的活跃变量被选出。相反，本综述中考虑的数据驱动惩罚函数方法不宜采用。而Tigress与LinSelect方法则属于保守型方法。