Likelihood-Based Nonparametric Causal Discovery under Latent Confounding

Learning causal structure from observational data in the presence of latent confounding remains a fundamental challenge in causal discovery. Acyclic directed mixed graphs (ADMGs) provide a natural representation of this problem by indicating causal effects and latent confounding via directed and bidirected edges. A line of recent work has focused on score-based approaches that formulate ADMG learning as continuous optimization problems with acyclicity and further structural constraints enforced through differentiable functions. However, the methods that were developed either focus on linear structural equations or lack computational and statistical tractability due to structural equations involving explicitly introduced latent confounders with general non-linear effects. In this work, we seek to trade-off the advantages of these two perspectives and propose causal models that relate the observed variables through non-linear structural equations but summarize confounding in mere noise correlations. For the proposed model class, we establish structural identifiability of bow-free graphs under a residual faithfulness assumption. Moreover, given a known ancestral graph, we clarify that the model parameters are identifiable. With this insight, we develop a novel likelihood-based ADMG learning framework. Importantly, our approach does not introduce explicit latent variables and, thus, necessitates disentangling correlations among noise terms and linear parts of causal effects, which we address using a non-linearity regularizer. Experiments show that our method outperforms existing state-of-the-art baselines on synthetic datasets while remaining competitive on real-world datasets.