The Complete Lasso Diagram

A fundamental problem in the high-dimensional regression is to understand the trade-off 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 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 trade-off 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 trade-off 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 trade-off diagram.

• Publication year

  2020

• Venue

  Unknown venue

• Publication date

  2020-07-21

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2007.11078
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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