Differentiable Structure Learning for Cyclic Linear Gaussian Models with Latent Confounders

The paper introduces a method for learning causal structures in linear Gaussian models that may contain directed cycles and an unknown number of latent confounders, bounded by a maximum. It derives the covariance of observed variables, defines marginal quasi-equivalence to identify when different models produce the same observational distributions, and formulates structure learning as a minimization of Gaussian negative log-likelihood with a complexity penalty counting edges and latent variables. Using Bernoulli gates to parameterize edge and latent inclusion, the authors obtain a closed‑form differentiable objective whose expected value shares the same global optimum as the discrete problem, and demonstrate experimentally that this approach yields lower recovery error than prior methods.

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