  We propose the group knockoff filter, a method for false discovery rate
control in a linear regression setting where the features are grouped, and we
would like to select a set of relevant groups which have a nonzero effect on
the response. By considering the set of true and false discoveries at the group
level, this method gains power relative to sparse regression methods. We also
apply our method to the multitask regression problem where multiple response
variables share similar sparsity patterns across the set of possible features.
Empirically, the group knockoff filter successfully controls false discoveries
at the group level in both settings, with substantially more discoveries made
by leveraging the group structure.
