# Extremely Greedy Equivalence Search

arXiv: https://arxiv.org/abs/2502.19551 · HTML: https://mlsanity.com/paper/2502.19551/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [Selective Greedy Equivalence Search: Finding Optimal Bayesian Networks Using a Polynomial Number of Score Evaluations](https://mlsanity.com/paper/1506.02113/) (2015)
- [On the pitfalls of Gaussian likelihood scoring for causal discovery](https://mlsanity.com/paper/2210.11104/) (2022)

## Built on by (most cited first, 8 of 8)

- [Causal-Copilot: An Autonomous Causal Analysis Agent](https://mlsanity.com/paper/2504.13263/) (2025)
- [Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning](https://mlsanity.com/paper/2510.04970/) (2025)
- [FoundCause: Causal Discovery with Latent Confounders from Observational Data](https://mlsanity.com/paper/2606.17516/) (2026)
- [Less Greedy Equivalence Search](https://mlsanity.com/paper/2506.22331/) (2025)
- [Practical Causal Evaluation Metrics for Biological Networks](https://mlsanity.com/paper/2511.12805/) (2025)
- [ORCA: An End-to-End Interactive Copilot for Optimized Root Cause Analysis](https://mlsanity.com/paper/2605.27022/) (2026)
- [StableRCA: Robust Graph-Agnostic Mechanism-Level Root Cause Analysis](https://mlsanity.com/paper/2606.05636/) (2026)
- [xWhyL: Causal Interactive Learning](https://mlsanity.com/paper/2609.26037/) (2026)

## Abstract (arXiv)

The goal of causal discovery is to learn a directed acyclic graph from data. One of the most well-known methods for this problem is Greedy Equivalence Search (GES). GES searches for the graph by incrementally and greedily adding or removing edges to maximize a model selection criterion. It has strong theoretical guarantees on infinite data but can fail in practice on finite data. In this paper, we first identify some of the causes of GES's failure, finding that it can get blocked in local optima, especially in denser graphs. We then propose eXtremely Greedy Equivalent Search (XGES), which involves a new heuristic to improve the search strategy of GES while retaining its theoretical guarantees. In particular, XGES favors deleting edges early in the search over inserting edges, which reduces the possibility of the search ending in local optima. A further contribution of this work is an efficient algorithmic formulation of XGES (and GES). We benchmark XGES on simulated datasets with known ground truth. We find that XGES consistently outperforms GES in recovering the correct graphs, and it is 10 times faster. XGES implementations in Python and C++ are available at https://github.com/ANazaret/XGES.