Causal discovery for linear causal model with correlated noise: an Adversarial Learning Approach

2026-01-04

arXiv.org

AI Summary

This work addresses the challenge of causal discovery in the presence of unobserved confounders—i.e., correlated noise—by proposing a novel method grounded in the f-GAN framework. The approach formulates causal structure learning as a Bayesian free energy minimization problem, which is equivalently recast as an f-divergence minimization and solved via adversarial learning to directly optimize binary graph structures within the discrete space of causal graphs. By leveraging the Gumbel-Softmax relaxation, the method circumvents reliance on explicit structural equation parameters, enabling end-to-end learning of causal graphs. Experimental results demonstrate that, under linear causal models, the proposed method effectively recovers true causal structures and achieves significantly improved robustness and accuracy in the presence of confounding interference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• causal discovery
• unmeasured confounding
• correlated noise
• linear causal model
• causal structure

Innovation

• causal discovery
• f-GAN
• adversarial learning
• unmeasured confounding
• Gumbel-Softmax