# DCILP: A Distributed Approach for Large-Scale Causal Structure Learning

arXiv: https://arxiv.org/abs/2406.10481 · HTML: https://mlsanity.com/paper/2406.10481/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 15 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Learning big Gaussian Bayesian networks: partition, estimation, and fusion](https://mlsanity.com/paper/1904.10900/) (2019)
- [Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets, and Complexity](https://mlsanity.com/paper/1605.04071/) (2016)

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

- [Causal-Copilot: An Autonomous Causal Analysis Agent](https://mlsanity.com/paper/2504.13263/) (2025)
- [Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation](https://mlsanity.com/paper/2509.19112/) (2025)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Multi-Agent Causal Reasoning System for Error Pattern Rule Automation in Vehicles](https://mlsanity.com/paper/2602.01155/) (2026)
- [Neural Autoregressive Flows for Markov Boundary Learning](https://mlsanity.com/paper/2603.20791/) (2026)
- [CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery](https://mlsanity.com/paper/2607.01936/) (2026)
- [Knowledge-Informed Local Causal Discovery of Optimal Adjustment Sets](https://mlsanity.com/paper/2607.04447/) (2026)
- [High-Order Markov Blanket Discovery via a k-Order Relaxation of the Faithfulness Assumption](https://mlsanity.com/paper/2607.26357/) (2026)

## Abstract (arXiv)

Causal learning tackles the computationally demanding task of estimating causal graphs. This paper introduces a new divide-and-conquer approach for causal graph learning, called DCILP. In the divide phase, the Markov blanket MB(Xi) of each variable Xi is identified, and causal learning subproblems associated with each MB(Xi) are independently addressed in parallel. This approach benefits from a more favorable ratio between the number of data samples and the number of variables considered. In counterpart, it can be adversely affected by the presence of hidden confounders, as variables external to MB(Xi) might influence those within it. The reconciliation of the local causal graphs generated during the divide phase is a challenging combinatorial optimization problem, especially in large-scale applications. The main novelty of DCILP is an original formulation of this reconciliation as an integer linear programming (ILP) problem, which can be delegated and efficiently handled by an ILP solver. Through experiments on medium to large scale graphs, and comparisons with state-of-the-art methods, DCILP demonstrates significant improvements in terms of computational complexity, while preserving the learning accuracy on real-world problem and suffering at most a slight loss of accuracy on synthetic problems.