# Large-Scale Differentiable Causal Discovery of Factor Graphs

arXiv: https://arxiv.org/abs/2206.07824 · HTML: https://mlsanity.com/paper/2206.07824/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 67 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 27 of 27)

- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [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)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Scaling structural learning with NO-BEARS to infer causal transcriptome networks](https://mlsanity.com/paper/1911.00081/) (2019)
- [The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data](https://mlsanity.com/paper/1910.05387/) (2019)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [Recent Developments in Boolean Matrix Factorization](https://mlsanity.com/paper/2012.03127/) (2020)
- [From graphs to DAGs: a low-complexity model and a scalable algorithm](https://mlsanity.com/paper/2204.04644/) (2022)
- [Structure Learning of Linear Gaussian Structural Equation Models with Weak Edges](https://mlsanity.com/paper/1707.07560/) (2017)
- [Binary Matrix Factorisation via Column Generation](https://mlsanity.com/paper/2011.04457/) (2020)
- [Identifying Seizure Onset Zone from the Causal Connectivity Inferred Using Directed Information](https://mlsanity.com/paper/1512.08309/) (2015)
- [Ranking Causal Influence of Financial Markets via Directed Information Graphs](https://mlsanity.com/paper/1801.06896/) (2018)

## Built on by (most cited first, 30 of 47)

- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modeling](https://mlsanity.com/paper/2211.03553/) (2022)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data](https://mlsanity.com/paper/2210.17283/) (2022)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [Sample, estimate, aggregate: A recipe for causal discovery foundation models](https://mlsanity.com/paper/2402.01929/) (2024)
- [Deep Learning of Causal Structures in High Dimensions](https://mlsanity.com/paper/2212.04866/) (2022)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [On the Identification of Temporally Causal Representation with Instantaneous Dependence](https://mlsanity.com/paper/2405.15325/) (2024)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Constraint-Free Structure Learning with Smooth Acyclic Orientations](https://mlsanity.com/paper/2309.08406/) (2023)
- [DCILP: A Distributed Approach for Large-Scale Causal Structure Learning](https://mlsanity.com/paper/2406.10481/) (2024)
- [The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data](https://mlsanity.com/paper/2308.15395/) (2023)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Large-Scale Targeted Cause Discovery via Learning from Simulated Data](https://mlsanity.com/paper/2408.16218/) (2024)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations](https://mlsanity.com/paper/2501.02409/) (2025)
- [Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm](https://mlsanity.com/paper/2405.18314/) (2024)
- [AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs](https://mlsanity.com/paper/2403.03772/) (2024)
- [ProDAG: Projected Variational Inference for Directed Acyclic Graphs](https://mlsanity.com/paper/2405.15167/) (2024)
- [Generative Intervention Models for Causal Perturbation Modeling](https://mlsanity.com/paper/2411.14003/) (2024)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Since Faithfulness Fails: The Performance Limits of Neural Causal Discovery](https://mlsanity.com/paper/2502.16056/) (2025)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [DiscoGen: Learning to Discover Gene Regulatory Networks](https://mlsanity.com/paper/2304.05823/) (2023)
- [Simulation-based Benchmarking for Causal Structure Learning in Gene Perturbation Experiments](https://mlsanity.com/paper/2407.06015/) (2024)
- [Characterization and Learning of Causal Graphs from Hard Interventions](https://mlsanity.com/paper/2505.01037/) (2025)
- [Causality-informed Anomaly Detection in Partially Observable Sensor Networks: Moving beyond Correlations](https://mlsanity.com/paper/2507.09742/) (2025)

## Abstract (arXiv)

A common theme in causal inference is learning causal relationships between observed variables, also known as causal discovery. This is usually a daunting task, given the large number of candidate causal graphs and the combinatorial nature of the search space. Perhaps for this reason, most research has so far focused on relatively small causal graphs, with up to hundreds of nodes. However, recent advances in fields like biology enable generating experimental data sets with thousands of interventions followed by rich profiling of thousands of variables, raising the opportunity and urgent need for large causal graph models. Here, we introduce the notion of factor directed acyclic graphs (f-DAGs) as a way to restrict the search space to non-linear low-rank causal interaction models. Combining this novel structural assumption with recent advances that bridge the gap between causal discovery and continuous optimization, we achieve causal discovery on thousands of variables. Additionally, as a model for the impact of statistical noise on this estimation procedure, we study a model of edge perturbations of the f-DAG skeleton based on random graphs and quantify the effect of such perturbations on the f-DAG rank. This theoretical analysis suggests that the set of candidate f-DAGs is much smaller than the whole DAG space and thus may be more suitable as a search space in the high-dimensional regime where the underlying skeleton is hard to assess. We propose Differentiable Causal Discovery of Factor Graphs (DCD-FG), a scalable implementation of -DAG constrained causal discovery for high-dimensional interventional data. DCD-FG uses a Gaussian non-linear low-rank structural equation model and shows significant improvements compared to state-of-the-art methods in both simulations as well as a recent large-scale single-cell RNA sequencing data set with hundreds of genetic interventions.