# Causal Inference Through the Structural Causal Marginal Problem

arXiv: https://arxiv.org/abs/2202.01300 · HTML: https://mlsanity.com/paper/2202.01300/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Nested Counterfactual Identification from Arbitrary Surrogate Experiments](https://mlsanity.com/paper/2107.03190/) (2021)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)

## Built on by (most cited first, 23 of 23)

- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Phenomenological Causality](https://mlsanity.com/paper/2211.09024/) (2022)
- [Counterfactual Causal Inference in Natural Language with Large Language Models](https://mlsanity.com/paper/2410.06392/) (2024)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Counterfactual Identifiability via Dynamic Optimal Transport](https://mlsanity.com/paper/2510.08294/) (2025)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Results on Counterfactual Invariance](https://mlsanity.com/paper/2307.08519/) (2023)
- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [Bounding probabilities of causation through the causal marginal problem](https://mlsanity.com/paper/2304.02023/) (2023)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [Estimating Joint Interventional Distributions from Marginal Interventional Data](https://mlsanity.com/paper/2409.01794/) (2024)
- [Tightening Bounds on Probabilities of Causation By Merging Datasets](https://mlsanity.com/paper/2310.08406/) (2023)
- [Variational Counterfactual Prediction under Runtime Domain Corruption](https://mlsanity.com/paper/2306.13271/) (2023)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)
- [Multi-Level Causal Embeddings](https://mlsanity.com/paper/2602.22287/) (2026)
- [Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome](https://mlsanity.com/paper/2608.10664/) (2026)
- [Same Predictions, Different Harms: Causal Auditing of Patient World Models](https://mlsanity.com/paper/2610.05198/) (2026)

## Abstract (arXiv)

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.