# Open problems in causal structure learning: A case study of COVID-19 in the UK

arXiv: https://arxiv.org/abs/2305.03859 · HTML: https://mlsanity.com/paper/2305.03859/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 116 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 26 of 26)

- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [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)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Properties of Bayesian Belief Network Learning Algorithms](https://mlsanity.com/paper/1302.6792/) (2013)
- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [Causal Modeling of Twitter Activity During COVID-19](https://mlsanity.com/paper/2005.07952/) (2020)
- [Bayesian network structure learning with causal effects in the presence of latent variables](https://mlsanity.com/paper/2005.14381/) (2020)
- [Learning Bayesian Networks that enable full propagation of evidence](https://mlsanity.com/paper/2004.04571/) (2020)
- [Effective and efficient structure learning with pruning and model averaging strategies](https://mlsanity.com/paper/2112.00398/) (2021)
- [Improving Bayesian Network Structure Learning in the Presence of Measurement Error](https://mlsanity.com/paper/2011.09776/) (2020)
- [Online Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1904.13247/) (2019)
- [A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks](https://mlsanity.com/paper/2007.03248/) (2020)
- [Tearing Apart NOTEARS: Controlling the Graph Prediction via Variance Manipulation](https://mlsanity.com/paper/2206.07195/) (2022)
- [Discovery and density estimation of latent confounders in Bayesian networks with evidence lower bound](https://mlsanity.com/paper/2206.05490/) (2022)

## Built on by (most cited first, 7 of 7)

- [Investigating potential causes of Sepsis with Bayesian network structure learning](https://mlsanity.com/paper/2406.09207/) (2024)
- [Using GPT-4 to guide causal machine learning](https://mlsanity.com/paper/2407.18607/) (2024)
- [Stable Structure Learning with HC-Stable and Tabu-Stable Algorithms](https://mlsanity.com/paper/2504.01740/) (2025)
- [Tuning structure learning algorithms with out-of-sample and resampling strategies](https://mlsanity.com/paper/2306.13932/) (2023)
- [Investigating the validity of structure learning algorithms in identifying risk factors for intervention in patients with diabetes](https://mlsanity.com/paper/2403.14327/) (2024)
- [Integrating Probabilistic Trees and Causal Networks for Clinical and Epidemiological Data](https://mlsanity.com/paper/2501.15973/) (2025)
- [Econometric vs. Causal Structure-Learning for Time-Series Policy Decisions: Evidence from the UK COVID-19 Policies](https://mlsanity.com/paper/2603.00041/) (2026)

## Abstract (arXiv)

Causal machine learning (ML) algorithms recover graphical structures that tell us something about cause-and-effect relationships. The causal representation praovided by these algorithms enables transparency and explainability, which is necessary for decision making in critical real-world problems. Yet, causal ML has had limited impact in practice compared to associational ML. This paper investigates the challenges of causal ML with application to COVID-19 UK pandemic data. We collate data from various public sources and investigate what the various structure learning algorithms learn from these data. We explore the impact of different data formats on algorithms spanning different classes of learning, and assess the results produced by each algorithm, and groups of algorithms, in terms of graphical structure, model dimensionality, sensitivity analysis, confounding variables, predictive and interventional inference. We use these results to highlight open problems in causal structure learning and directions for future research. To facilitate future work, we make all graphs, models, data sets, and source code publicly available online.