The use of simulated data in the field of causal discovery is ubiquitous due
to the scarcity of annotated real data. Recently, Reisach et al., 2021
highlighted the emergence of patterns in simulated linear data, which displays
increasing marginal variance in the casual direction. As an ablation in their
experiments, Montagna et al., 2023 found that similar patterns may emerge in
nonlinear models for the variance of the score vector $\nabla \log
p_{\mathbf{X}}$, and introduced the ScoreSort algorithm. In this work, we
formally define and characterize this score-sortability pattern of nonlinear
additive noise models. We find that it defines a class of identifiable
(bivariate) causal models overlapping with nonlinear additive noise models. We
theoretically demonstrate the advantages of ScoreSort in terms of statistical
efficiency compared to prior state-of-the-art score matching-based methods and
empirically show the score-sortability of the most common synthetic benchmarks
in the literature. Our findings remark (1) the lack of diversity in the data as
an important limitation in the evaluation of nonlinear causal discovery
approaches, (2) the importance of thoroughly testing different settings within
a problem class, and (3) the importance of analyzing statistical properties in
causal discovery, where research is often limited to defining identifiability
conditions of the model.

利用模拟数据在因果发现领域普遍存在，本文对线性数据和非线性模型中方差的演变模式进行了研究，并引入了 ScoreSort 算法。通过理论和实证分析发现 ScoreSort 在统计效率上相较于之前的方法具有优势，认为缺乏数据多样性限制了非线性因果发现方法的评估，强调了在问题类中进行不同设置的全面测试的重要性，以及分析因果发现中的统计特性的重要性，现有研究常限于模型的可识别性条件。