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.

本研究使用最优传递（OT）来研究从数据中学习因果结构的问题，提供了一种基于下三角单调参数传输映射的约束方法来设计对噪声分布无偏置的条件独立性检验，还提供了一种可以处理潜在变量的因果发现算法，并使用一种新方法来定义分数，与现有技术进行了实验结果比较。

通过单调三角输运映射学习因果图