# Estimating and Controlling the False Discovery Rate for the PC Algorithm Using Edge-Specific P-Values

arXiv: https://arxiv.org/abs/1607.03975 · HTML: https://mlsanity.com/paper/1607.03975/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2016.

## Built on by (most cited first, 8 of 8)

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- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [Empirically Calibrated Conditional Independence Tests](https://mlsanity.com/paper/2602.21036/) (2026)
- [Step-by-Step Causality: Transparent Causal Discovery with Multi-Agent Tree-Query and Adversarial Confidence Estimation](https://mlsanity.com/paper/2601.10137/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)
- [Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey](https://mlsanity.com/paper/2608.11156/) (2026)

## Abstract (arXiv)

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.