No More Maybe-Arrows: Resolving Causal Uncertainty by Breaking Symmetries

2026-03-01

AI Summary

Observational data typically identify the true causal directed acyclic graph (DAG) only up to a Markov equivalence class, resulting in ambiguity that hinders downstream applications. This work proposes CausalSAGE, a novel framework that, for the first time, precisely refines a partial ancestral graph (PAG) into a unique DAG by leveraging state-level variable expansion and a symmetry-breaking mechanism. The approach integrates structural knowledge with soft prior constraints to narrow the search space, employs a unified differentiable objective for joint optimization of causal structure, and enforces acyclicity to guarantee valid outputs. The resulting DAG not only faithfully recovers the underlying causal relationships but also demonstrates high computational efficiency and scalability, substantially outperforming existing PAG refinement methods.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The recent works on causal discovery have followed a similar trend of learning partial ancestral graphs (PAGs) since observational data constrain the true causal directed acyclic graph (DAG) only up to a Markov equivalence class. This limits their application in the majority of downstream tasks, as uncertainty in causal relations remains unresolved. We propose a new refinement framework, CausalSAGE, for converting PAGs to DAGs while respecting the underlying causal relations. The framework expands discrete variables into state-level representations, constrains the search space using structural knowledge and soft priors, and applies a unified differentiable objective for joint optimization. The final DAG is obtained by aggregating the optimized structures and enforcing acyclicity when necessary. Our experimental evaluations show that the obtained DAGs preserve the underlying causal relations while also being efficient to obtain.

Problem

• causal discovery
• partial ancestral graph
• directed acyclic graph
• causal uncertainty
• Markov equivalence class

Innovation

• Causal Discovery
• Partial Ancestral Graph
• Markov Equivalence Class
• Differentiable Optimization
• CausalSAGE