Estimating the causal structure of observational data is a challenging combinatorial search problem that scales super-exponentially with graph size. Existing methods use continuous relaxations to make this problem computationally tractable but often restrict the data-generating process to additive noise models (ANMs) through explicit or implicit assumptions. We present Order-based Structure Learning with Normalizing Flows (OSLow), a framework that relaxes these assumptions using autoregressive normalizing flows. We leverage the insight that searching over topological orderings is a natural way to enforce acyclicity in structure discovery and propose a novel, differentiable permutation learning method to find such orderings. Through extensive experiments on synthetic and real-world data, we demonstrate that OSLow outperforms prior baselines and improves performance on the observational Sachs and SynTReN datasets as measured by structural hamming distance and structural intervention distance, highlighting the importance of relaxing the ANM assumption made by existing methods.

翻译：估计观测数据的因果结构是一个具有挑战性的组合搜索问题，其复杂度随图大小呈超指数增长。现有方法通过连续松弛使该问题在计算上可行，但通常通过显式或隐式假设将数据生成过程限制为加性噪声模型（ANMs）。我们提出基于序的结构学习与归一化流（OSLow）框架，该框架利用自回归归一化流放宽上述假设。我们利用拓扑排序搜索天然具有强制结构发现中无环性的特性，并提出一种新颖的可微排序学习方法以寻找此类拓扑序。通过在合成数据和真实数据上的大量实验，我们证明OSLow优于现有基准方法，并在观测性Sachs和SynTReN数据集上显著提升了结构汉明距离与结构干预距离指标的性能，这凸显了放宽现有方法所依赖的ANM假设的重要性。