# Improving Efficiency and Accuracy of Causal Discovery Using a Hierarchical Wrapper

arXiv: https://arxiv.org/abs/2107.05001 · HTML: https://mlsanity.com/paper/2107.05001/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 11 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Neuropathic Pain Diagnosis Simulator for Causal Discovery Algorithm Evaluation](https://mlsanity.com/paper/1906.01732/) (2019)
- [Selective Greedy Equivalence Search: Finding Optimal Bayesian Networks Using a Polynomial Number of Score Evaluations](https://mlsanity.com/paper/1506.02113/) (2015)
- [The Reduced PC-Algorithm: Improved Causal Structure Learning in Large Random Networks](https://mlsanity.com/paper/1806.06209/) (2018)
- [SADA: A General Framework to Support Robust Causation Discovery with Theoretical Guarantee](https://mlsanity.com/paper/1707.01283/) (2017)
- [Bayesian Structure Learning by Recursive Bootstrap](https://mlsanity.com/paper/1809.04828/) (2018)

## Built on by (most cited first, 6 of 6)

- [Causal Interpretation of Self-Attention in Pre-Trained Transformers](https://mlsanity.com/paper/2310.20307/) (2023)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)
- [A Causal World Model Underlying Next Token Prediction: Exploring GPT in a Controlled Environment](https://mlsanity.com/paper/2412.07446/) (2024)
- [CLEAR: Causal Explanations from Attention in Neural Recommenders](https://mlsanity.com/paper/2210.10621/) (2022)

## Abstract (arXiv)

Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete causal discovery algorithms have been previously introduced, where a directed acyclic graph (DAG), or its equivalence class, representing causal relations is searched. However, in real-world cases, only finite training data is available, which limits the power of statistical tests used by these algorithms, leading to errors in the inferred causal model. This is commonly addressed by devising a strategy for using as few as possible statistical tests. In this paper, we introduce such a strategy in the form of a recursive wrapper for existing constraint-based causal discovery algorithms, which preserves soundness and completeness. It recursively clusters the observed variables using the normalized min-cut criterion from the outset, and uses a baseline causal discovery algorithm during backtracking for learning local sub-graphs. It then combines them and ensures completeness. By an ablation study, using synthetic data, and by common real-world benchmarks, we demonstrate that our approach requires significantly fewer statistical tests, learns more accurate graphs, and requires shorter run-times than the baseline algorithm.