完整的Lasso权衡图
The Complete Lasso Tradeoff Diagram
摘要：
高维回归中的一个基本问题是理解I型和II型错误之间的权衡，或者等价地，变量选择中的错误发现率（FDR）和功率。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，区分所有对的FDR和电源，可以渐近实现的套索与一些选择其罚参数从剩余的对，在一个政权的线性稀疏随机设计。无论信号有多强，我们的图所表征的FDR和功率之间的权衡都成立。特别是，我们的研究结果提高了早期的Lasso权衡图arXiv：1511.01957通过识别两个简单的，但基本的限制对FDR和电源。当回归问题在Donoho-Tanner相变之上时，改进更显著。最后，我们提出了广泛的模拟研究，以确认完整的套索权衡图的清晰度。
英文摘要：
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.
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