  The PC algorithm allows investigators to estimate a complete partially
directed acyclic graph (CPDAG) from a finite dataset, but few groups have
investigated strategies for estimating and controlling the false discovery rate
(FDR) of the edges in the CPDAG. In this paper, we introduce PC with p-values
(PC-p), a fast algorithm which robustly computes edge-specific p-values and
then estimates and controls the FDR across the edges. PC-p specifically uses
the p-values returned by many conditional independence tests to upper bound the
p-values of more complex edge-specific hypothesis tests. The algorithm then
estimates and controls the FDR using the bounded p-values and the
Benjamini-Yekutieli FDR procedure. Modifications to the original PC algorithm
also help PC-p accurately compute the upper bounds despite non-zero Type II
error rates. Experiments show that PC-p yields more accurate FDR estimation and
control across the edges in a variety of CPDAGs compared to alternative
methods.
