Differentiable Causal Discovery of Linear Non-Gaussian Acyclic Models Under Unmeasured Confounding

Abstract

We propose a score-based method that extends the framework of the linear non- Gaussian acyclic model (LiNGAM) to address the problem of causal structure estimation in the presence of unmeasured variables. Building on the method pro- posed by Bhattacharya et al. (2021), we develop a method called ABIC LiNGAM, which assumes that error terms follow a multivariate generalized normal distribu- tion and employs continuous optimization techniques to recover acyclic directed mixed graphs (ADMGs). We demonstrate that the proposed method can esti- mate causal structures, including the possibility of identifying their orientations, rather than only Markov equivalence classes, under the assumption that the data are linear and follow a multivariate generalized normal distribution. Additionally, we provide proofs of the identifiability of the parameters in ADMGs when the er- ror terms follow a multivariate generalized normal distribution. The effectiveness of the proposed method is validated through simulations and experiments using real-world data.