[論文レビュー] Causal discovery for linear causal model with correlated noise: an Adversarial Learning Approach

Mujin Zhou, Junzhe Zhang|arXiv (Cornell University)|Jan 4, 2026

Bayesian Modeling and Causal Inference被引用数 0

ひとこと要約

The paper proposes fGAN-CD, a causal structure learning method for linear SEMs with unmeasured confounding, formulating structure learning as Bayesian free energy minimization and solving via an f-GAN with Gumbel-Softmax relaxation to infer ADMGs.

ABSTRACT

Causal discovery from data with unmeasured confounding factors is a challenging problem. This paper proposes an approach based on the f-GAN framework, learning the binary causal structure independent of specific weight values. We reformulate the structure learning problem as minimizing Bayesian free energy and prove that this problem is equivalent to minimizing the f-divergence between the true data distribution and the model-generated distribution. Using the f-GAN framework, we transform this objective into a min-max adversarial optimization problem. We implement the gradient search in the discrete graph space using Gumbel-Softmax relaxation.

研究の動機と目的

• Infer binary causal structure M=(S_B, S_Σ) for linear SEMs with unmeasured confounding.
• Minimize Bayesian free energy F(X|M) to select the optimal graph structure.
• Transform structure learning into an f-divergence minimization problem and solve via adversarial training.

提案手法

• Represent causal structure with binary adjacency components S_B (directed edges) and S_Σ (confounding correlations).
• Use Bayesian free energy minimization, which is equivalent to minimizing KL(P_data || q(·|M)).
• Recast KL minimization as an f-GAN variational divergence minimization with a discriminative network.
• Apply Gumbel-Softmax relaxation to enable differentiable optimization over discrete graph structures.
• Train a generator G that samples from the marginal distribution q(·|M) by masking sampled weights with learned structures.
• Use a differentiable acyclicity constraint h(Ã_B) via relaxed structures to enforce DAG-ness

実験結果

リサーチクエスチョン

• RQ1 Can Bayesian free energy minimization identify the underlying ADMG among general structures with unmeasured confounding?
• RQ2 Does an f-GAN-based adversarial objective effectively minimize the KL divergence between P_data and the model distribution q(·|M) for causal graphs?
• RQ3 Can Gumbel-Softmax relaxation enable gradient-based learning of discrete causal graphs while enforcing acyclicity?
• RQ4 How does fGAN-CD perform in recovering directed edges and confounding edges compared to existing baselines under synthetic data?

主な発見

Method	SHD \u000219	Skeleton F1	Arrowhead F1
ABIC	3.4	0.897	0.1
fGAN-CD	2.17	0.909	0.667

• fGAN-CD learns ADMG structures without restricting to bow-free constraints or Arid subclasses.
• The method improves structural recovery over ABIC in case studies, especially for correctly identifying arrow directions.
• In a high-confounding sparsity test, fGAN-CD correctly excludes non-existent edges (e.g., 0 and 3) where ABIC erroneously connects them.
• Experiments show fGAN-CD yields competitive SHD and higher Skeleton F1 and Arrowhead F1 than ABIC in the reported case study.
• The paper demonstrates that the framework handles general ADMGs and dense confounding better than the baseline.