Synthetic datasets generated by structural causal models (SCMs) are commonly used for benchmarking causal structure learning algorithms. However, the variances and pairwise correlations in SCM data tend to increase along the causal ordering. Several popular algorithms exploit these artifacts, possibly leading to conclusions that do not generalize to real-world settings. Existing metrics like $\operatorname{Var}$-sortability and $\operatorname{R^2}$-sortability quantify these patterns, but they do not provide tools to remedy them. To address this, we propose internally-standardized structural causal models (iSCMs), a modification of SCMs that introduces a standardization operation at each variable during the generative process. By construction, iSCMs are not $\operatorname{Var}$-sortable. We also find empirical evidence that they are mostly not $\operatorname{R^2}$-sortable for commonly-used graph families. Moreover, contrary to the post-hoc standardization of data generated by standard SCMs, we prove that linear iSCMs are less identifiable from prior knowledge on the weights and do not collapse to deterministic relationships in large systems, which may make iSCMs a useful model in causal inference beyond the benchmarking problem studied here. Our code is publicly available at: https://github.com/werkaaa/iscm.

翻译：由结构因果模型（SCMs）生成的合成数据集通常用于基准测试因果结构学习算法。然而，SCM数据中的方差和成对相关性往往沿着因果顺序增加。几种流行算法利用了这些人为特征，可能导致结论无法推广到现实世界场景。现有指标如$\operatorname{Var}$-可排序性和$\operatorname{R^2}$-可排序性量化了这些模式，但未提供修正工具。为此，我们提出内部标准化结构因果模型（iSCMs），这是一种对SCMs的改进，在生成过程中为每个变量引入了标准化操作。通过构造，iSCMs不具备$\operatorname{Var}$-可排序性。我们还发现经验证据表明，对于常用图族，iSCMs大多也不具备$\operatorname{R^2}$-可排序性。此外，与对标准SCMs生成数据进行事后标准化相反，我们证明线性iSCMs从权重先验知识中更难被识别，且不会在大系统中坍缩为确定性关系，这可能使iSCMs成为因果推断中一个有用的模型，超越本文研究的基准测试问题。我们的代码公开于：https://github.com/werkaaa/iscm。