Estimating and Controlling the False Discovery Rate of the PC Algorithm Using Edge-specific P-Values

Abstract

Many causal discovery algorithms infer graphical structure from observational data. The PC algorithm in particular estimates a completed partially directed acyclic graph (CPDAG), or an acyclic graph containing directed edges identifiable with conditional independence testing. However, few groups have investigated strategies for estimating and controlling the false discovery rate (FDR) of the edges in the CPDAG. In this article, we introduce PC with p-values (PC-p), a fast algorithm that 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 (CI) 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.