# Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)

arXiv: https://arxiv.org/abs/2406.10537 · HTML: https://mlsanity.com/paper/2406.10537/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 15 Jun 2024.

## Builds on (most cited first, 23 of 23)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Ordering-Based Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1910.09014/) (2019)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approach](https://mlsanity.com/paper/2310.06680/) (2023)
- [Computably Continuous Reinforcement-Learning Objectives are PAC-learnable](https://mlsanity.com/paper/2303.05518/) (2023)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [XInsight: eXplainable Data Analysis Through The Lens of Causality](https://mlsanity.com/paper/2207.12718/) (2022)
- [PerfCE: Performance Debugging on Databases with Chaos Engineering-Enhanced Causality Analysis](https://mlsanity.com/paper/2207.08369/) (2022)
- [Causality-Aided Trade-off Analysis for Machine Learning Fairness](https://mlsanity.com/paper/2305.13057/) (2023)
- [Enabling Runtime Verification of Causal Discovery Algorithms with Automated Conditional Independence Reasoning (Extended Version)](https://mlsanity.com/paper/2309.05264/) (2023)

## Built on by (most cited first, 6 of 6)

- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [FoundCause: Causal Discovery with Latent Confounders from Observational Data](https://mlsanity.com/paper/2606.17516/) (2026)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)
- [Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning](https://mlsanity.com/paper/2601.05474/) (2026)
- [Demistifying Data and Simulator Assumptions in Supervised Causal Discovery](https://mlsanity.com/paper/2609.37446/) (2026)
- [Differentiable Structure Learning for Cyclic Linear Gaussian Models with Latent Confounders](https://mlsanity.com/paper/2609.38618/) (2026)

## Abstract (arXiv)

Differentiable causal discovery has made significant advancements in the learning of directed acyclic graphs. However, its application to real-world datasets remains restricted due to the ubiquity of latent confounders and the requirement to learn maximal ancestral graphs (MAGs). To date, existing differentiable MAG learning algorithms have been limited to small datasets and failed to scale to larger ones (e.g., with more than 50 variables). The key insight in this paper is that the causal skeleton, which is the undirected version of the causal graph, has potential for improving accuracy and reducing the search space of the optimization procedure, thereby enhancing the performance of differentiable causal discovery. Therefore, we seek to address a two-fold challenge to harness the potential of the causal skeleton for differentiable causal discovery in the presence of latent confounders: (1) scalable and accurate estimation of skeleton and (2) universal integration of skeleton estimation with differentiable causal discovery. To this end, we propose SPOT (Skeleton Posterior-guided OpTimization), a two-phase framework that harnesses skeleton posterior for differentiable causal discovery in the presence of latent confounders. On the contrary to a ``point-estimation'', SPOT seeks to estimate the posterior distribution of skeletons given the dataset. It first formulates the posterior inference as an instance of amortized inference problem and concretizes it with a supervised causal learning (SCL)-enabled solution to estimate the skeleton posterior. To incorporate the skeleton posterior with differentiable causal discovery, SPOT then features a skeleton posterior-guided stochastic optimization procedure to guide the optimization of MAGs. [abridged due to length limit]