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 estimate causal structures, including their orientations, rather than only Markov equivalence classes, under the assumption that the data are linear and follow a multivariate gen- eralized normal distribution. Additionally, we provide proofs of the identifiability of the parameters in ADMGs when the error terms follow a multivariate gener- alized normal distribution. The effectiveness of the proposed method is validated through simulations and experiments using real-world data.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Sergey_Plis1
Submission Number: 4056
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