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

Tingrui Huang, Devendra Singh Dhami

TL;DR

This work proposes a new refinement framework, CausalSAGE, for converting PAGs to DAGs while respecting the underlying causal relations, and shows that the obtained DAGs preserve the underlying causal relations while also being efficient to obtain.

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.

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

TL;DR

This work proposes a new refinement framework, CausalSAGE, for converting PAGs to DAGs while respecting the underlying causal relations, and shows that the obtained DAGs preserve the underlying causal relations while also being efficient to obtain.

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.
Paper Structure (72 sections, 45 equations, 6 figures, 11 tables, 1 algorithm)

This paper contains 72 sections, 45 equations, 6 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. CausalSAGE
  4. State-Aware Representation
  5. State Expansion.
  6. Block-wise Parameterization.
  7. Structural Encoding of PAG
  8. Variable-level admissibility.
  9. State-level lifting.
  10. Likelihood-Based Direction Selection
  11. Reconstruction signal.
  12. State-level logit construction.
  13. Block strength aggregation (for edge interpretation and extraction).
  14. Cross-entropy reconstruction objective.
  15. Structural Regularization
  16. ...and 57 more sections

Figures (6)

  • Figure 1: Why PAGs are not enough. (a) Most downstream tasks require a fully specified causal DAG. (b) FCI handles latent confounders but outputs partially oriented graphs (PAGs). (c) Ambiguous parent sets (e.g., $\mathrm{Pa}(X)$) prevent computing interventional effects.
  • Figure 2: CausalSAGE. The framework expands discrete variables into state representations, constrains the search space using random/LLM priors, and finally applies a unified differentiable objective for joint optimization to output a DAG.
  • Figure 3: SHD reduction via refinement (Q1). Bars show $\Delta$SHD = (Baseline $-$ Refined), where the positive values indicate improvement.
  • Figure 4: Elimination of Orientation Ambiguity. FCI/RFCI leaves a large fraction of edges unresolved (46%–86%) across datasets. CausalSAGE reduces this ratio to 0% in all cases, effectively breaking Markov equivalence and producing fully directed DAGs.
  • Figure 5: Comparison with standard DAG learners (10k samples). SHD measures structural error, while F1 measures directional accuracy. Points closer to the top-left corner indicate stronger overall performance.
  • ...and 1 more figures