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

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.