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The optimal predictive rule is the conditional response function Graph HT ht . Start with a set of I n i training samples, and divide them into I K i evenly sized and non-overlapping folds Graph HT ht . We have access to a stream independent and identically distributed samples Graph HT ht with Graph HT ht and Graph HT ht . [Extracted from the article]

We enjoyed reading Professor Efron's (Brad) paper just as much as we enjoyed listening to his June 2019 lecture in Leiden. Interestingly, Efron puts the pure predictive algorithms to the test in a scenario where the sample size is extremely moderate by today's standards ( I n i = 102). In the knockoff framework, one can use I any i black-box (any predictive model) to identify any kind possible association - linear or not - between a large set of explanatory variables Graph HT ht and an outcome I Y i . This framework rigorously tests whether the conditional distribution Graph HT ht actually depends on any of the variables I X SB j sb i without assuming any model for how I X i and I Y i are connected (Candès et al. [4]). [Extracted from the article]