The framework of knockoffs has been recently proposed to perform variable selection
under rigorous type-I error control, without relying on strong modeling assumptions.
We extend the methodology of knockoffs to a rich family of problems where
the distribution of the covariates can be described by a hidden Markov
model. We develop an exact and efficient algorithm to sample
knockoff variables in this setting and then argue that, combined with the existing
selective framework, this provides a natural and powerful
tool for performing principled inference in genome-wide association
studies with guaranteed false discovery rate control.
This is joint work with Matteo Sesia and Emmanuel Candes.
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