# ExMAG: Learning of Maximally Ancestral Graphs

arXiv: https://arxiv.org/abs/2503.08245 · HTML: https://mlsanity.com/paper/2503.08245/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 60 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Instrumental Variables: An Econometrician's Perspective](https://mlsanity.com/paper/1410.0163/) (2014)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding](https://mlsanity.com/paper/2004.03758/) (2020)
- [A factorization criterion for acyclic directed mixed graphs](https://mlsanity.com/paper/1406.6764/) (2014)
- [Causal network learning with non-invertible functional relationships](https://mlsanity.com/paper/2004.09646/) (2020)
- [Deconfounding and Causal Regularization for Stability and External Validity](https://mlsanity.com/paper/2008.06234/) (2020)
- [A fast score-based search algorithm for maximal ancestral graphs using entropy](https://mlsanity.com/paper/2402.04777/) (2024)
- [Towards standard imsets for maximal ancestral graphs](https://mlsanity.com/paper/2208.10436/) (2022)
- [Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams](https://mlsanity.com/paper/2406.09049/) (2024)
- [ExDAG: an MIQP Algorithm for Learning DAGs](https://mlsanity.com/paper/2406.15229/) (2024)

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

- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)

## Abstract (arXiv)

In mixed graphs, there are both directed and bidirected edges. An extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. This extension is of considerable interest in causal learning in the presence of confounders. There, directed edges represent a clear direction of causality, while bidirected edges represent confounding. We propose a branch-and-cut algorithm for learning maximally ancestral graphs using a formulation as a mixed-integer quadratic program. Empirically, our method achieves comparable or improved reconstruction quality while requiring an order of magnitude fewer samples than state-of-the-art approaches.