# How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors

arXiv: https://arxiv.org/abs/2502.14719 · HTML: https://mlsanity.com/paper/2502.14719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Improving Accuracy and Scalability of the PC Algorithm by Maximizing P-value](https://mlsanity.com/paper/1610.00378/) (2016)
- [Do causal predictors generalize better to new domains?](https://mlsanity.com/paper/2402.09891/) (2024)
- [Quantitative probing: Validating causal models using quantitative domain knowledge](https://mlsanity.com/paper/2209.03013/) (2022)
- [A cautious approach to constraint-based causal model selection](https://mlsanity.com/paper/2404.18232/) (2024)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Are you doing better than random guessing? A call for using negative controls when evaluating causal discovery algorithms](https://mlsanity.com/paper/2412.10039/) (2024)
- [Choosing DAG Models Using Markov and Minimal Edge Count in the Absence of Ground Truth](https://mlsanity.com/paper/2409.20187/) (2024)

## Built on by (most cited first, 1 of 1)

- [TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations](https://mlsanity.com/paper/2605.03045/) (2026)

## Abstract (arXiv)

Causal discovery methods based on the PC algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first analyze how local errors can propagate throughout the output graph of a PC-based method, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that can be detected by comparable existing methods. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.