# Recursive Causal Discovery

arXiv: https://arxiv.org/abs/2403.09300 · HTML: https://mlsanity.com/paper/2403.09300/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 91 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 30 of 35)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [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)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Ordering-Based Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1910.09014/) (2019)
- [Efficient Intervention Design for Causal Discovery with Latents](https://mlsanity.com/paper/2005.11736/) (2020)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression](https://mlsanity.com/paper/1511.08963/) (2015)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Penalized Estimation of Directed Acyclic Graphs From Discrete Data](https://mlsanity.com/paper/1403.2310/) (2014)
- [Advances in Learning Bayesian Networks of Bounded Treewidth](https://mlsanity.com/paper/1406.1411/) (2014)

## Built on by (most cited first, 12 of 12)

- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Does TabPFN Understand Causal Structures?](https://mlsanity.com/paper/2511.07236/) (2025)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [Graph Learning Is Suboptimal in Causal Bandits](https://mlsanity.com/paper/2510.16811/) (2025)
- [QWO: Speeding Up Permutation-Based Causal Discovery in LiGAMs](https://mlsanity.com/paper/2410.23155/) (2024)
- [Traceable Latent Variable Discovery Based on Multi-Agent Collaboration](https://mlsanity.com/paper/2602.14456/) (2026)
- [On the Number of Conditional Independence Tests in Constraint-based Causal Discovery](https://mlsanity.com/paper/2603.21844/) (2026)
- [Neural Autoregressive Flows for Markov Boundary Learning](https://mlsanity.com/paper/2603.20791/) (2026)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)
- [Decoupled Causal Discovery](https://mlsanity.com/paper/2609.23535/) (2026)
- [Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models](https://mlsanity.com/paper/2609.24241/) (2026)

## Abstract (arXiv)

Causal discovery, i.e., learning the causal graph from data, is often the first step toward the identification and estimation of causal effects, a key requirement in numerous scientific domains. Causal discovery is hampered by two main challenges: limited data results in errors in statistical testing and the computational complexity of the learning task is daunting. This paper builds upon and extends four of our prior publications (Mokhtarian et al., 2021; Akbari et al., 2021; Mokhtarian et al., 2022, 2023a). These works introduced the concept of removable variables, which are the only variables that can be removed recursively for the purpose of causal discovery. Presence and identification of removable variables allow recursive approaches for causal discovery, a promising solution that helps to address the aforementioned challenges by reducing the problem size successively. This reduction not only minimizes conditioning sets in each conditional independence (CI) test, leading to fewer errors but also significantly decreases the number of required CI tests. The worst-case performances of these methods nearly match the lower bound. In this paper, we present a unified framework for the proposed algorithms, refined with additional details and enhancements for a coherent presentation. A comprehensive literature review is also included, comparing the computational complexity of our methods with existing approaches, showcasing their state-of-the-art efficiency. Another contribution of this paper is the release of RCD, a Python package that efficiently implements these algorithms. This package is designed for practitioners and researchers interested in applying these methods in practical scenarios. The package is available at github.com/ban-epfl/rcd, with comprehensive documentation provided at rcdpackage.com.