Nonlinear causal discovery from observational data imposes strict identifiability assumptions on the formulation of structural equations utilized in the data generating process. The evaluation of structure learning methods under assumption violations requires a rigorous and interpretable approach, which quantifies both the structural similarity of the estimation with the ground truth and the capacity of the discovered graphs to be used for causal inference. Motivated by the lack of unified performance assessment framework, we introduce an interpretable, six-dimensional evaluation metric, i.e., distance to optimal solution (DOS), which is specifically tailored to the field of causal discovery. Furthermore, this is the first research to assess the performance of structure learning algorithms from seven different families on increasing percentage of non-identifiable, nonlinear causal patterns, inspired by real-world processes. Our large-scale simulation study, which incorporates seven experimental factors, shows that besides causal order-based methods, amortized causal discovery delivers results with comparatively high proximity to the optimal solution. In addition to the findings from our sensitivity analysis, we explore interactions effects between the experimental factors of our simulation framework in order to provide transparency about the expected performance of causal discovery techniques in different scenarios.

本研究解决了在假设违背情况下，如何评估结构学习方法的有效性这一问题。我们提出了一种可解释的六维评估指标“最优解距离”（DOS），以全面评估因果发现中的结构相似性。研究表明，除了基于因果顺序的方法外，摊销因果发现与最优解的接近度也相对较高，为因果发现技术的性能提供了新的洞见。

我们对独立同分布数据的结构学习了解多少？可解释的多维因果发现性能指标