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Asaf WEINSTEIN (Carnegie Mellon University) – “A power analysis for knockoffs using Lasso and thresholded-Lasso statistics”
April 8, 2019, 3:00 pm - 4:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 8th of April 2019
Place: Room 3001.
Asaf WEINSTEIN (Carnegie Mellon University) – “A power analysis for knockoffs using Lasso and thresholded-Lasso statistics“
Abstract : Practitioners using the Lasso are well aware of its limitations as a variable selector. That good prediction usually leads to many falsely selected variables implies that to capture most of the signal, one necessarily pays with a high number of false positives. It is also well known that this situation can be mitigated by thresholding the Lasso estimates, i.e., by discarding small estimates one can reduce considerably the number of false selections.
Recent works have studied both these phenomena from a theoretical perspective in the approximate message-passing (AMP) framework, providing exact asymptotic predictions for Type I and Type II error rates. These existing works are important because they allow to answer both quantitative and qualitative questions (for example, where to stop on the Lasso path to ensure FDR\leq \alpha, or at which value of \lambda should the thresholded Lasso estimates be computed for optimal power?) and compare Lasso to Thresholded Lasso. However, many of these answers depend on the distribution of the underlying signal. In this talk I’ll focus on our experience with using Knockoffs to mimic these oracle procedures in the absence of knowledge about the signal. It will be demonstrated that the sensitivity of power to the fraction of fake variables added, is very different for Lasso and for Thresholded Lasso.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM