# Deep Learning of Causal Structures in High Dimensions

arXiv: https://arxiv.org/abs/2212.04866 · HTML: https://mlsanity.com/paper/2212.04866/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Evaluation of Causal Structure Learning Algorithms via Risk Estimation](https://mlsanity.com/paper/2006.15387/) (2020)
- [Ancestral causal learning in high dimensions with a human genome-wide application](https://mlsanity.com/paper/1905.11506/) (2019)

## Built on by (most cited first, 20 of 20)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)
- [Response Theory via Generative Score Modeling](https://mlsanity.com/paper/2402.01029/) (2024)
- [Simulation-based Benchmarking for Causal Structure Learning in Gene Perturbation Experiments](https://mlsanity.com/paper/2407.06015/) (2024)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [No Foundations without Foundations -- Why semi-mechanistic models are essential for regulatory biology](https://mlsanity.com/paper/2501.19178/) (2025)
- [Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements](https://mlsanity.com/paper/2310.11147/) (2023)
- [Towards Graph Prompt Learning: A Survey and Beyond](https://mlsanity.com/paper/2408.14520/) (2024)
- [Causally-Aware Unsupervised Feature Selection Learning](https://mlsanity.com/paper/2410.12224/) (2024)
- [Causal Graph Neural Networks for Healthcare](https://mlsanity.com/paper/2511.02531/) (2025)
- [Causally-informed Deep Learning towards Explainable and Generalizable Outcomes Prediction in Critical Care](https://mlsanity.com/paper/2502.02109/) (2025)
- [TSCAN: Context-Aware Uplift Modeling via Two-Stage Training for Online Merchant Business Diagnosis](https://mlsanity.com/paper/2504.18881/) (2025)
- [DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlation](https://mlsanity.com/paper/2506.11653/) (2025)
- [Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences](https://mlsanity.com/paper/2511.10031/) (2025)
- [Noise-robust Contrastive Learning for Critical Transition Detection in Dynamical Systems](https://mlsanity.com/paper/2512.12523/) (2025)
- [Many Experiments, Few Repetitions, Unpaired Data, and Sparse Effects: Is Causal Inference Possible?](https://mlsanity.com/paper/2601.15254/) (2026)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)
- [Causal Cellular Context Transfer Learning (C3TL): An Efficient Architecture for Prediction of Unseen Perturbation Effects](https://mlsanity.com/paper/2603.13051/) (2026)
- [On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models](https://mlsanity.com/paper/2603.27406/) (2026)
- [Learning Individual Dynamics from Sparse Cross-Sectional Snapshots](https://mlsanity.com/paper/2605.23470/) (2026)

## Abstract (arXiv)

Recent years have seen rapid progress at the intersection between causality and machine learning. Motivated by scientific applications involving high-dimensional data, in particular in biomedicine, we propose a deep neural architecture for learning causal relationships between variables from a combination of empirical data and prior causal knowledge. We combine convolutional and graph neural networks within a causal risk framework to provide a flexible and scalable approach. Empirical results include linear and nonlinear simulations (where the underlying causal structures are known and can be directly compared against), as well as a real biological example where the models are applied to high-dimensional molecular data and their output compared against entirely unseen validation experiments. These results demonstrate the feasibility of using deep learning approaches to learn causal networks in large-scale problems spanning thousands of variables.