# A General Framework on Conditions for Constraint-based Causal Learning

arXiv: https://arxiv.org/abs/2408.07575 · HTML: https://mlsanity.com/paper/2408.07575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [On the Equivalence of Causal Models](https://mlsanity.com/paper/1304.1108/) (2013)
- [Conditions and Assumptions for Constraint-based Causal Structure Learning](https://mlsanity.com/paper/2103.13521/) (2021)
- [Localised Natural Causal Learning Algorithms for Weak Consistency Conditions](https://mlsanity.com/paper/2402.14775/) (2024)

## Abstract (arXiv)

Most constraint-based causal learning algorithms provably return the correct causal graph under certain correctness conditions, such as faithfulness. By representing any constraint-based causal learning algorithm using the notion of a property, we provide a general framework to obtain and study correctness conditions for these algorithms. From the framework, we provide exact correctness conditions for the PC algorithm, which are then related to the correctness conditions of some other existing causal discovery algorithms. The framework also suggests a paradigm for designing causal learning algorithms which allows for the correctness conditions of algorithms to be controlled for before designing the actual algorithm, and has the following implications. We show that the sparsest Markov representation condition is the weakest correctness condition for algorithms that output ancestral graphs or directed acyclic graphs satisfying any existing notions of minimality. We also reason that Pearl-minimality is necessary for meaningful causal learning but not sufficient to relax the faithfulness condition and, as such, has to be strengthened, such as by including background knowledge, for causal learning beyond faithfulness.