UCLA

Recent advances in causal learning have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model assumptions, rely heavily on general independence tests, or require substantial computation. To address these limitations, we propose a sequential procedure to orient undirected edges in a completed partial DAG (CPDAG), representing an equivalence class of DAGs, by leveraging a pairwise additive noise model (PANM) to identify their causal directions. We prove that this procedure can recover the true causal DAG assuming a restricted ANM. Building on this result, we develop a novel constraint-based algorithm for learning causal DAGs under nonlinear ANMs. Given an estimated CPDAG, we develop a ranking procedure that sorts undirected edges by their adherence to the PANM, which defines an evaluation order of the edges. To determine the edge direction, we devise a statistical test that compares the log-likelihood values, evaluated with respect to the competing directions, of a sub-graph comprising just the candidate nodes and their identified parents in the partial DAG. We further establish the structural learning consistency of our algorithm in the large-sample limit. Extensive experiments on synthetic and real-world data sets demonstrate that our method is computationally efficient, robust to model misspecification, and consistently outperforms many existing nonlinear DAG learning methods. We also study nonlinear causal structure learning in the presence of latent variables, where the latent projection of a DAG is represented by an acyclic directed mixed graph (ADMGs). Existing approaches are often limited by model assumptions and rely on iterative testing. To this end, we develop a sequential edge orientation framework for determining undetermined edges in a partial ancestral graph (PAG) that combines the strengths of constraint-based and score-based methods. We propose a graphical criterion for identifying edges whose orientations can be correctly inferred through conditional independence tests, enabling targeted edge evaluation rather than repeated global testing. For the remaining edges, we directly compare competing orientations using log-likelihood estimates obtained through a parameter estimation procedure tailored to nonlinear models that more accurately recovers the covariance structure. Through extensive simulations, we demonstrate that the proposed framework substantially improves the recovery of both causal and latent confounding relationships and achieves greater accuracy than existing competing methods.