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

2025-11-17

AI Summary

This paper addresses the challenge of counterfactual probability inference in semi-Markov structural causal models (SCMs), where latent confounders—exogenous variables affecting multiple endogenous variables—induce non-Markovian dependencies. We propose the first divide-and-conquer algorithm tailored to semi-Markov SCMs: leveraging structural equation specifications, we decompose the model into causally isolated submodels; perform exact counterfactual inference on each; and aggregate results via boundary propagation to handle uncertainty arising from high-cardinality exogenous variable distributions. Theoretical analysis and empirical evaluation demonstrate that our method efficiently computes tight counterfactual probability bounds while substantially reducing computational complexity without sacrificing accuracy. Our key contribution is extending the divide-and-conquer paradigm beyond Markov SCMs—previously limited to acyclic, no-latent-confounding settings—to semi-Markov SCMs with latent confounding. This establishes a scalable, verifiable framework for counterfactual reasoning in complex systems with unobserved confounding.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Recently, Bjøru 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 extit{semi-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.

Problem

• Extends causal inference from Markovian to semi-Markovian structural models
• Addresses confounding relationships through exogenous variable decomposition
• Develops strategies for bounding counterfactual probabilities with confounding

Innovation

• Divide-and-conquer algorithm for bounding counterfactual probabilities
• Extending methodology to semi-Markovian structural causal models
• Decomposing models with high-cardinality into precise sub-models