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Activity Number: 13 - Recent Progress on Knockoffs Theory and Applications
Type: Invited
Date/Time: Monday, August 3, 2020 : 10:00 AM to 11:50 AM
Sponsor: IMS
Abstract #309485
Title: Controlling for Confounders Through Approximate Sufficiency
Author(s): Rina Foygel Barber* and Lucas Janson
Companies: University of Chicago and Harvard University
Keywords:
Abstract:

We consider the problem of testing conditional independence between X (a feature of interest) and Y (a response variable), conditioned on confounding variables Z. Recent work by Huang & Janson (2019) establishes that, if the distribution of X conditional on Z is known up to a low-dimensional parameter, then valid knockoff copies of the feature X may be drawn by conditioning on the sufficient statistics of X given Z. In some settings, however, the sufficient statistics already fully determine X - two important examples are when X consists of binary data, and for instance follows a logistic model given Z, or if X given Z follows a mixture model such as a mixture of Gaussians. In these settings, the control group (the knockoff copies of X) is then identical to the real data, and the resulting method is unable to make discoveries. Our new results show that we can instead use the notion of approximate sufficiency, conditioning on weaker information to achieve strong power while retaining asymptotic validity of the Type I error control.


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