# Differentiable Causal Discovery Under Unmeasured Confounding

arXiv: https://arxiv.org/abs/2010.06978 · HTML: https://mlsanity.com/paper/2010.06978/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 30 of 56)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [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)
- [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)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [CausalCity: Complex Simulations with Agency for Causal Discovery and Reasoning](https://mlsanity.com/paper/2106.13364/) (2021)
- [Truncated Matrix Power Iteration for Differentiable DAG Learning](https://mlsanity.com/paper/2208.14571/) (2022)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [DoWhy: Addressing Challenges in Expressing and Validating Causal Assumptions](https://mlsanity.com/paper/2108.13518/) (2021)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Causal Graph Discovery with Retrieval-Augmented Generation based Large Language Models](https://mlsanity.com/paper/2402.15301/) (2024)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysis](https://mlsanity.com/paper/2306.02831/) (2023)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Expert-Aided Causal Discovery of Ancestral Graphs](https://mlsanity.com/paper/2309.12032/) (2023)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Causal Additive Models with Unobserved Causal Paths and Backdoor Paths](https://mlsanity.com/paper/2502.07646/) (2025)
- [Discovering Dynamic Causal Space for DAG Structure Learning](https://mlsanity.com/paper/2306.02822/) (2023)
- [psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learning](https://mlsanity.com/paper/2410.23862/) (2024)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)

## Abstract (arXiv)

The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset. Code implementing our methods is open-source and publicly available at https://gitlab.com/rbhatta8/dcd and will be incorporated into the Ananke package.