# Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning

arXiv: https://arxiv.org/abs/2406.06348 · HTML: https://mlsanity.com/paper/2406.06348/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [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)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Clustering and Community Detection in Directed Networks: A Survey](https://mlsanity.com/paper/1308.0971/) (2013)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Learning big Gaussian Bayesian networks: partition, estimation, and fusion](https://mlsanity.com/paper/1904.10900/) (2019)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [Partitioned hybrid learning of Bayesian network structures](https://mlsanity.com/paper/2103.12188/) (2021)

## Built on by (most cited first, 4 of 4)

- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)
- [Efficient Causal Structure Learning via Modular Subgraph Integration](https://mlsanity.com/paper/2601.21014/) (2026)
- [Causal Discovery for Cross-Sectional Data Based on Super-Structure and Divide-and-Conquer](https://mlsanity.com/paper/2602.03914/) (2026)
- [A phenotype-driven and evidence-governed framework for knowledge graph enrichment and hypotheses discovery in population data](https://mlsanity.com/paper/2604.16982/) (2026)

## Abstract (arXiv)

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way -- without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure -- a set of learned or existing candidate hypotheses -- to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to 104 variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces.