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**Abstract**: Two years ago in this workshop I presented my work on model-X knockoffs, a method for high-dimensional variable selection that provides exact (finite-sample) control of false discoveries and high power as a result of its flexibility to leverage any and all domain knowledge and tools from machine learning to search for signal. In this talk, I will discuss two recent works that significantly advance the usability and generality of model-X knockoffs. First, I will show how the original assumptions of model-X knockoffs, that the multivariate distribution of the covariates be known exactly, can be significantly relaxed to the assumption that only a *model* for the covariates be known, and that model can have as many free parameters as the *product* of the sample size and dimension. No loss in the guarantees of knockoffs is incurred by this relaxation of the assumptions. Second, I will show how to efficiently and exactly sample knockoffs for *any *distribution on the covariates, even if the distribution is only known up to a normalization constant. This dramatically expands the set of covariate distribution for which we can apply knockoffs. This is joint work with a number of collaborators, listed below in the full references for the two works:

D. Huang and L. Janson. Relaxing the Assumptions of Knockoffs by Conditioning. Annals of Statistics (to appear), 2019.

S. Bates, E. Candès, L. Janson, and W. Wang. Metropolized Knockoff Sampling. 2019.