We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional independence tests which are agnostic to the noise distribution. We provide an algorithm for causal discovery up to Markov Equivalence with no assumptions on the structural equations/noise distributions, which allows for settings with latent variables. Our approach also extends to score-based causal discovery by providing a novel means for defining scores. This allows us to uniquely recover the causal graph under additional identifiability and structural assumptions, such as additive noise or post-nonlinear models. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world datasets.

翻译：我们研究利用最优传输（OT）从数据中学习因果关系结构的问题。具体而言，我们首先提出一种基于约束的方法，该方法借助下三角单调参数化传输图设计对噪声分布不敏感的独立性检验。我们提供了一种因果发现算法，可在不对结构方程/噪声分布作任何假设的情况下，达到马尔可夫等价类的识别水平，且能处理包含潜变量的场景。本研究通过提供一种定义分数的全新途径，将所提方法扩展至基于分数的因果发现。这使得我们能在附加可识别性及结构假设（如加性噪声模型或后非线性模型）下，唯一恢复因果图。我们通过实验将所提方法与现有最优方法在合成数据集和真实数据集上进行了比较。