Title: A power analysis for Knockoffs with lasso statistics
Authors: Asaf Weinstein - Stanford University (United States) [presenting]
Rina Foygel Barber - University of Chicago (United States)
Emmanuel Candes - Stanford (United States)
Abstract: Knockoffs is a new framework for controlling the false discovery rate (FDR) in multiple hypothesis testing problems involving complex statistical models. While rigorous results have been obtained regarding type-I error control in a wide range of models, type-II error rates have been far less studied. In general, power calculations are admittedly difficult, in part owing to the very particular structure of the knockoff matrix. Nevertheless, there is a specific setting, involving an i.i.d. Gaussian design, where such calculations are possible. Working in that setting, we leverage recent results to show that a knockoff procedure associated with the Lasso path, achieves close to optimal power with respect to an appropriately defined oracle. This result demonstrates that, in our setting, augmenting the design with fake (knockoff) variables does not have a high cost in terms of power.