# On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models

arXiv: https://arxiv.org/abs/2502.08531 · HTML: https://mlsanity.com/paper/2502.08531/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 69 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [pgmpy: A Python Toolkit for Bayesian Networks](https://mlsanity.com/paper/2304.08639/) (2023)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Near-Optimal Learning of Tree-Structured Distributions by Chow-Liu](https://mlsanity.com/paper/2011.04144/) (2020)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression](https://mlsanity.com/paper/1511.08963/) (2015)
- [Improving Accuracy and Scalability of the PC Algorithm by Maximizing P-value](https://mlsanity.com/paper/1610.00378/) (2016)
- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Toward Falsifying Causal Graphs Using a Permutation-Based Test](https://mlsanity.com/paper/2305.09565/) (2023)
- [Separation-based distance measures for causal graphs](https://mlsanity.com/paper/2402.04952/) (2024)
- [Estimating and Controlling the False Discovery Rate for the PC Algorithm Using Edge-Specific P-Values](https://mlsanity.com/paper/1607.03975/) (2016)
- [Recovering Causal Structures from Low-Order Conditional Independencies](https://mlsanity.com/paper/2010.02675/) (2020)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Argumentative Causal Discovery](https://mlsanity.com/paper/2405.11250/) (2024)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [Structural perspective on constraint-based learning of Markov networks](https://mlsanity.com/paper/2403.08562/) (2024)

## Built on by (most cited first, 3 of 3)

- [On the Number of Conditional Independence Tests in Constraint-based Causal Discovery](https://mlsanity.com/paper/2603.21844/) (2026)
- [Learning Bayesian and Markov Networks with an Unreliable Oracle](https://mlsanity.com/paper/2603.09563/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)

## Abstract (arXiv)

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to errors and violated assumptions. Often, there are tests that were not used in the construction of the graph. In this work, we show that these redundant tests have the potential to detect or sometimes correct errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions.