论文标题
完整的套索权衡图
The Complete Lasso Tradeoff Diagram
论文作者
论文摘要
高维回归中的一个基本问题是了解I型和II型错误之间的权衡，或者等效地，错误的发现率（FDR）和可变选择中的权力。为了解决这个重要的问题，我们提供了第一个完整的权衡图，该图可以区分所有成对的FDR和功率，而在随机设计下，在线性稀疏方案中，套件可以选择其罚款参数与其余对的某种惩罚参数。无论信号有多强大，我们图表的FDR与功率之间的权衡都具有。特别是，通过认识到FDR和Power对的两个简单但基本的限制，我们的结果改善了Arxiv的早期拉索权衡图：1511.01957。当回归问题高于Donoho--Tanner相转变时，改善将更加实质性。最后，我们提出了广泛的仿真研究，以确认完整的拉索权衡图的清晰度。
A fundamental problem in the high-dimensional regression is to understand the tradeoff between type I and type II errors or, equivalently, false discovery rate (FDR) and power in variable selection. To address this important problem, we offer the first complete tradeoff diagram that distinguishes all pairs of FDR and power that can be asymptotically realized by the Lasso with some choice of its penalty parameter from the remaining pairs, in a regime of linear sparsity under random designs. The tradeoff between the FDR and power characterized by our diagram holds no matter how strong the signals are. In particular, our results improve on the earlier Lasso tradeoff diagram of arXiv:1511.01957 by recognizing two simple but fundamental constraints on the pairs of FDR and power. The improvement is more substantial when the regression problem is above the Donoho--Tanner phase transition. Finally, we present extensive simulation studies to confirm the sharpness of the complete Lasso tradeoff diagram.
