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Characterizing the Type 1-Type 2 Error Trade-off for SLOPE

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Friday, March 25, 2022
3:30 pm - 4:30 pm
Cynthia Rush, Assistant Professor, Columbia University, Statistics
Statistical Science Seminar Series

Sorted L1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this talk, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I and type II error. Additionally, we show that on any problem instance, SLOPE with a certain regularization sequence outperforms the Lasso, in the sense of having a smaller FDP, larger TPP and smaller L2 estimation risk simultaneously. Our proofs are based on a novel technique that reduces a variational calculus problem to a class of infinite-dimensional convex optimization problems and a very recent result from approximate message passing (AMP) theory. With SLOPE being a particular example, we discuss these results in the context of a general program for systematically deriving exact expressions for the asymptotic risk of estimators that are solutions to a broad class of convex optimization problems via AMP.

Collaborators on this work include Zhiqi Bu, Jason Klusowski, and Weijie Su ( and and Oliver Feng, Ramji Venkataramanan, and Richard Samworth (

This will be a virtual event. It will be held in 116 Old Chemistry and it will be on zoom.
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Meeting ID: 923 9738 2385
Passcode: 425966