# Structural Causal Models Are (Solvable by) Credal Networks

arXiv: https://arxiv.org/abs/2008.00463 · HTML: https://mlsanity.com/paper/2008.00463/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2020.

## Built on by (most cited first, 22 of 22)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Causally Reliable Concept Bottleneck Models](https://mlsanity.com/paper/2503.04363/) (2025)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources](https://mlsanity.com/paper/2307.16577/) (2023)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Bounding Counterfactuals under Selection Bias](https://mlsanity.com/paper/2208.01417/) (2022)
- [Robust Counterfactual Inference in Markov Decision Processes](https://mlsanity.com/paper/2502.13731/) (2025)
- [Tractable Bounding of Counterfactual Queries by Knowledge Compilation](https://mlsanity.com/paper/2310.03352/) (2023)
- [Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Models](https://mlsanity.com/paper/2509.03548/) (2025)
- [CREPO: An Open Repository to Benchmark Credal Network Algorithms](https://mlsanity.com/paper/2105.04158/) (2021)
- [Robustness Guarantees for Credal Bayesian Networks via Constraint Relaxation over Probabilistic Circuits](https://mlsanity.com/paper/2205.05793/) (2022)
- [Bayesian Networks for Causal Analysis in Socioecological Systems](https://mlsanity.com/paper/2401.10101/) (2024)
- [Causal computations in Semi Markovian Structural Causal Models using divide and conquer](https://mlsanity.com/paper/2511.13852/) (2025)
- [Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions](https://mlsanity.com/paper/2602.18762/) (2026)
- [Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Data](https://mlsanity.com/paper/2212.02932/) (2022)
- [A Framework for Causal Concept-based Model Explanations](https://mlsanity.com/paper/2512.02735/) (2025)
- [On the Relationship between Bayesian Networks and Probabilistic Structural Causal Models](https://mlsanity.com/paper/2603.27406/) (2026)
- [Optimal Experiments for Partial Causal Effect Identification](https://mlsanity.com/paper/2605.06993/) (2026)
- [Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information](https://mlsanity.com/paper/2607.04957/) (2026)

## Abstract (arXiv)

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.