Recent advances 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 computational time. 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 the 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 datasets demonstrate that our method is computationally efficient, robust to model misspecification, and consistently outperforms many existing nonlinear DAG learning methods.

翻译：最近的进展确立了加性噪声模型下无环有向图的可识别性，这推动了各种因果发现方法的发展。然而，现有方法大多施加了严格的模型假设，严重依赖通用独立性检验，或需要大量计算时间。为解决这些局限，我们提出一种序列过程，通过利用成对加性噪声模型来识别完整偏有向无环图（表示有向无环图等价类）中无向边的因果方向。我们证明，在受限加性噪声模型假设下，该过程能恢复真实的因果有向无环图。基于此结果，我们开发了一种新颖的基于约束的算法，用于学习非线性加性噪声模型下的因果有向无环图。给定估计的完整偏有向无环图，我们设计了一种排序过程，根据无向边对成对加性噪声模型的符合程度对其排序，这定义了边的评估顺序。为确定边的方向，我们提出一种统计检验方法，比较子图（仅包含候选节点及其在偏有向无环图中已识别的父节点）在竞争方向下的对数似然值。此外，我们在大样本极限下确立了算法的结构学习一致性。在合成数据集和真实世界数据集上的大量实验表明，我们的方法计算高效、对模型误设鲁棒，并在性能上始终优于许多现有的非线性有向无环图学习方法。