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

TL;DR

This paper introduces an adversarial learning approach using f-GANs for causal discovery in linear models with correlated noise, effectively learning causal structures despite unmeasured confounders.

Contribution

It reformulates causal structure learning as a Bayesian free energy minimization and employs an adversarial framework with Gumbel-Softmax relaxation for discrete graph optimization.

Findings

Successfully models causal structures with correlated noise.

Proves equivalence between free energy minimization and f-divergence.

Employs Gumbel-Softmax for gradient-based discrete graph search.

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.