标题： 实际中的高维回归：有限样本预测、变量选择和排序的实证研究 显示英文标题

标题： High-dimensional regression in practice: an empirical study of finite-sample prediction, variable selection and ranking

摘要： 惩罚似然方法广泛用于高维回归问题。尽管许多方法已被提出且相关的理论现已得到很好的发展，但在实际应用中有限样本设置下不同方法的相对有效性仍未能完全理解。因此，该领域需要实证研究以提供实用的见解和指导。本文中，我们对惩罚回归方法进行了大规模比较。我们将三个相关目标区分开来：预测、变量选择和变量排序。我们的结果涵盖了超过2300种数据生成场景，包括合成数据和半合成数据（真实协变量和模拟响应），使我们能够系统地考虑各种因素（样本大小、维度、稀疏性、信号强度和多重共线性）的影响。我们考虑了几种广泛使用的方法（Lasso、自适应Lasso、弹性网络、岭回归、SCAD、Dantzig选择器和稳定性选择）。我们发现不同方法之间的性能存在显著差异。我们的结果支持“没有灵丹妙药”的观点，在所有情景和目标中没有一种明确的优胜者，即使在这种所有数据都很好地符合方法假设的受限情况下也是如此。本研究使我们能够根据目标和某些数据特性推荐哪些方法可能最（或最不适合）。我们的经验结果补充了现有的理论，并提供了一个资源，用于在多种场景和指标下比较方法。 显示英文摘要

摘要： Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample settings, as encountered in practice, remains incompletely understood. There is therefore a need for empirical investigations in this area that can offer practical insight and guidance to users. In this paper we present a large-scale comparison of penalized regression methods. We distinguish between three related goals: prediction, variable selection and variable ranking. Our results span more than 2,300 data-generating scenarios, including both synthetic and semi-synthetic data (real covariates and simulated responses), allowing us to systematically consider the influence of various factors (sample size, dimensionality, sparsity, signal strength and multicollinearity). We consider several widely-used approaches (Lasso, Adaptive Lasso, Elastic Net, Ridge Regression, SCAD, the Dantzig Selector and Stability Selection). We find considerable variation in performance between methods. Our results support a `no panacea' view, with no unambiguous winner across all scenarios or goals, even in this restricted setting where all data align well with the assumptions underlying the methods. The study allows us to make some recommendations as to which approaches may be most (or least) suitable given the goal and some data characteristics. Our empirical results complement existing theory and provide a resource to compare methods across a range of scenarios and metrics.