# Causal computations in Semi Markovian Structural Causal Models using divide and conquer

arXiv: https://arxiv.org/abs/2511.13852 · HTML: https://mlsanity.com/paper/2511.13852/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [Structural Causal Models Are (Solvable by) Credal Networks](https://mlsanity.com/paper/2008.00463/) (2020)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [Approximate Causal Effect Identification under Weak Confounding](https://mlsanity.com/paper/2306.13242/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Framework for Causal Concept-based Model Explanations](https://mlsanity.com/paper/2512.02735/) (2025)

## Abstract (arXiv)

Recently, Bjoru et al. proposed a novel divide-and-conquer algorithm for bounding counterfactual probabilities in structural causal models (SCMs). They assumed that the SCMs were learned from purely observational data, leading to an imprecise characterization of the marginal distributions of exogenous variables. Their method leveraged the canonical representation of structural equations to decompose a general SCM with high-cardinality exogenous variables into a set of sub-models with low-cardinality exogenous variables. These sub-models had precise marginals over the exogenous variables and therefore admitted efficient exact inference. The aggregated results were used to bound counterfactual probabilities in the original model. The approach was developed for Markovian models, where each exogenous variable affects only a single endogenous variable. In this paper, we investigate extending the methodology to textitsemi-Markovian SCMs, where exogenous variables may influence multiple endogenous variables. Such models are capable of representing confounding relationships that Markovian models cannot. We illustrate the challenges of this extension using a minimal example, which motivates a set of alternative solution strategies. These strategies are evaluated both theoretically and through a computational study.