  Testing multiple hypotheses of conditional independence with provable error
rate control is a fundamental problem with various applications. To infer
conditional independence with family-wise error rate (FWER) control when only
summary statistics of marginal dependence are accessible, we adopt
GhostKnockoff to directly generate knockoff copies of summary statistics and
propose a new filter to select features conditionally dependent to the response
with provable FWER control. In addition, we develop a computationally efficient
algorithm to greatly reduce the computational cost of knockoff copies
generation without sacrificing power and FWER control. Experiments on simulated
data and a real dataset of Alzheimer's disease genetics demonstrate the
advantage of proposed method over the existing alternatives in both statistical
power and computational efficiency.
