# Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams

arXiv: https://arxiv.org/abs/2406.09049 · HTML: https://mlsanity.com/paper/2406.09049/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 8 of 8)

- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [Structure Learning for Cyclic Linear Causal Models](https://mlsanity.com/paper/2006.05978/) (2020)
- [Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams](https://mlsanity.com/paper/1508.01717/) (2015)
- [Smooth, identifiable supermodels of discrete DAG models with latent variables](https://mlsanity.com/paper/1511.06813/) (2015)
- [Ananke: A Python Package For Causal Inference Using Graphical Models](https://mlsanity.com/paper/2301.11477/) (2023)
- [Graphical Representations for Algebraic Constraints of Linear Structural Equations Models](https://mlsanity.com/paper/2208.00926/) (2022)

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

- [ExMAG: Learning of Maximally Ancestral Graphs](https://mlsanity.com/paper/2503.08245/) (2025)

## Abstract (arXiv)

For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In the setting of linear structural equation models without bows, we study algebraic constraints and argue that these provide the most fine-grained resolution achievable. We propose efficient algorithms that decide whether two graphs impose the same algebraic constraints, or whether the constraints imposed by one graph are a subset of those imposed by another graph.