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The Complete Lasso Tradeoff Diagram
Hua Wang · Yachong Yang · Zhiqi Bu · Weijie Su

Tue Dec 08 08:10 PM -- 08:20 PM (PST) @ Orals & Spotlights: Deep Learning/Theory
in Orals & Spotlights Track 13: Deep Learning/Theory »

A fundamental problem in 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 diagram that distinguishes all pairs of FDR and power that can be asymptotically realized by the Lasso 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 complete the earlier Lasso tradeoff diagram in previous literature by recognizing two simple 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.

Author Information

Hua Wang (Wharton School, University of Pennsylvania)
Yachong Yang (University of Pennsylvania)
Zhiqi Bu (University of Pennsylvania)
Weijie Su (The Wharton School, University of Pennsylvania)

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