We propose OCDaf, a novel order-based method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for non-constant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate state-of-the-art performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance (SHD) and Structural Intervention Distance (SID). Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines.

翻译：我们提出OCDaf，一种新颖的基于顺序的方法，用于从观测数据中学习因果图。我们在多元异方差噪声模型中建立了因果图的可辨识性，这是加性噪声模型的一种推广，允许噪声方差非常数。利用这些模型与仿射自回归归一化流之间的结构相似性，我们引入了一种连续搜索算法来发现因果结构。我们的实验在Sachs和SynTReN基准测试中展示了在结构汉明距离（SHD）和结构干预距离（SID）方面的最先进性能。此外，我们通过各种参数和非参数合成数据集验证了可辨识性理论，并展示了相比现有基线方法的优越性能。